Calculate probability P ( F − ) and explain its meaning.

Question

Want to see more full solutions like this?

Answer 1

Question

Chapter 5, Problem 95CE

i.

To determine

Calculate probability P(F−) and explain its meaning.

i.

Expert Solution

Answer to Problem 95CE

The probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Explanation of Solution

Calculation:

The given table shows that frequencies of the actual and predicted interest rate movements.

The given contingency table is,

	Actual Change
Forecast Change	Decline (A–)	Rise (A+)	Row Total
Decline (F–)	7	12	19
Rise (F+)	9	6	15
Column Total	16	18	34

The formula for finding the probability P(F−) is,

P(F−)=Frequency for the class F−Total frequencies in the distribution.

Substitute 19 for ‘Frequency for the class F–’ and 34 for ‘Total frequencies in the distribution’

P(F−)=1934=0.5588

Therefore, the probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

ii.

To determine

Calculate probability P(A+) and explain its meaning.

ii.

Expert Solution

Answer to Problem 95CE

The probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+) is,

P(A+)=Frequency for the class A+Total frequencies in the distribution

Substitute 18 for ‘Frequency for the class A+’ and 34 for ‘Total frequencies in the distribution’

P(A+)=1834=0.5294

Therefore, the probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

iii.

To determine

Calculate probability P(A−|F−) and explain its meaning.

iii.

Expert Solution

Answer to Problem 95CE

The probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Explanation of Solution

Calculation:

The formula for finding the probability P(A−|F−) is,

P(A−|F−)=Frequency for the class A− and F−Frequency for the class F−

Substitute 7 for ‘Frequency for the class A– and F–’ and 19 for ‘Frequency for the class F–’,

P(A−|F−)=719=0.3684

Therefore, the probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

iv.

To determine

Calculate probability P(A+|F+) and explain its meaning.

iv.

Expert Solution

Answer to Problem 95CE

The probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+|F+) is,

P(A+|F+)=Frequency for the class A+ and F+Frequency for the class F+

Substitute 6 for ‘Frequency for the class A+ and F+’ and 15 for ‘Frequency for the class F+’,

P(A+|F+)=615=0.4

Therefore, the probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

v.

To determine

Calculate probability P(A+ and F+) and explain its meaning.

v.

Expert Solution

Answer to Problem 95CE

The probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+ and F+) is,

P(A+ and F+)=Frequency for the class A+ and F+Total frequencies in the distribution

Substitute 6 for ‘Frequency for the class A+ and F+’ and 34 for ‘Total frequencies in the distribution’,

P(A+ and F+)=634=0.1765

Therefore, the probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

vi.

To determine

Calculate probability P(A− and F−) and explain its meaning.

vi.

Expert Solution

Answer to Problem 95CE

The probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Explanation of Solution

Calculation:

The formula for finding the probability P(A− and F−) is,

P(A− and F−)=Frequency for the class A− and F−Total frequencies in the distribution

Substitute 7 for ‘Frequency for the class A– and F–’ and 34 for ‘Total frequencies in the distribution’,

P(A− and F−)=734=0.2059

Therefore, the probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

Suppose you are gambling on a roulette wheel. Each time the wheel is spun, the result is one of the outcomes 0, 1, and so on through 36. Of these outcomes, 18 are red, 18 are black, and 1 is green. On each spin you bet $5 that a red outcome will occur and $1 that the green outcome will occur. If red occurs, you win a net $4. (You win $10 from red and nothing from green.) If green occurs, you win a net $24. (You win $30 from green and nothing from red.) If black occurs, you lose everything you bet for a loss of $6. a. Use simulation to generate 1,000 plays from this strategy. Each play should indicate the net amount won or lost. Then, based on these outcomes, calculate a 95% confidence interval for the total net amount won or lost from 1,000 plays of the game. (Round your answers to two decimal places and if your answer is negative value, enter "minus" sign.) I worked out the Upper Limit, but I can't seem to arrive at the correct answer for the Lower Limit. What is the Lower Limit?…

Let us suppose we have some article reported on a study of potential sources of injury to equine veterinarians conducted at a university veterinary hospital. Forces on the hand were measured for several common activities that veterinarians engage in when examining or treating horses. We will consider the forces on the hands for two tasks, lifting and using ultrasound. Assume that both sample sizes are 6, the sample mean force for lifting was 6.2 pounds with standard deviation 1.5 pounds, and the sample mean force for using ultrasound was 6.4 pounds with standard deviation 0.3 pounds. Assume that the standard deviations are known. Suppose that you wanted to detect a true difference in mean force of 0.25 pounds on the hands for these two activities. Under the null hypothesis, 40 0. What level of type II error would you recommend here? = Round your answer to four decimal places (e.g. 98.7654). Use α = 0.05. β = 0.0594 What sample size would be required? Assume the sample sizes are to be…

Consider the hypothesis test Ho: 0 s² = = 4.5; s² = 2.3. Use a = 0.01. = σ against H₁: 6 > σ2. Suppose that the sample sizes are n₁ = 20 and 2 = 8, and that (a) Test the hypothesis. Round your answers to two decimal places (e.g. 98.76). The test statistic is fo = 1.96 The critical value is f = 6.18 Conclusion: fail to reject the null hypothesis at a = 0.01. (b) Construct the confidence interval on 02/2/622 which can be used to test the hypothesis: (Round your answer to two decimal places (e.g. 98.76).) 035

Answer 2

Question

Chapter 5, Problem 95CE

i.

To determine

Calculate probability P(F−) and explain its meaning.

i.

Expert Solution

Answer to Problem 95CE

The probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Explanation of Solution

Calculation:

The given table shows that frequencies of the actual and predicted interest rate movements.

The given contingency table is,

	Actual Change
Forecast Change	Decline (A–)	Rise (A+)	Row Total
Decline (F–)	7	12	19
Rise (F+)	9	6	15
Column Total	16	18	34

The formula for finding the probability P(F−) is,

P(F−)=Frequency for the class F−Total frequencies in the distribution.

Substitute 19 for ‘Frequency for the class F–’ and 34 for ‘Total frequencies in the distribution’

P(F−)=1934=0.5588

Therefore, the probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

ii.

To determine

Calculate probability P(A+) and explain its meaning.

ii.

Expert Solution

Answer to Problem 95CE

The probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+) is,

P(A+)=Frequency for the class A+Total frequencies in the distribution

Substitute 18 for ‘Frequency for the class A+’ and 34 for ‘Total frequencies in the distribution’

P(A+)=1834=0.5294

Therefore, the probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

iii.

To determine

Calculate probability P(A−|F−) and explain its meaning.

iii.

Expert Solution

Answer to Problem 95CE

The probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Explanation of Solution

Calculation:

The formula for finding the probability P(A−|F−) is,

P(A−|F−)=Frequency for the class A− and F−Frequency for the class F−

Substitute 7 for ‘Frequency for the class A– and F–’ and 19 for ‘Frequency for the class F–’,

P(A−|F−)=719=0.3684

Therefore, the probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

iv.

To determine

Calculate probability P(A+|F+) and explain its meaning.

iv.

Expert Solution

Answer to Problem 95CE

The probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+|F+) is,

P(A+|F+)=Frequency for the class A+ and F+Frequency for the class F+

Substitute 6 for ‘Frequency for the class A+ and F+’ and 15 for ‘Frequency for the class F+’,

P(A+|F+)=615=0.4

Therefore, the probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

v.

To determine

Calculate probability P(A+ and F+) and explain its meaning.

v.

Expert Solution

Answer to Problem 95CE

The probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+ and F+) is,

P(A+ and F+)=Frequency for the class A+ and F+Total frequencies in the distribution

Substitute 6 for ‘Frequency for the class A+ and F+’ and 34 for ‘Total frequencies in the distribution’,

P(A+ and F+)=634=0.1765

Therefore, the probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

vi.

To determine

Calculate probability P(A− and F−) and explain its meaning.

vi.

Expert Solution

Answer to Problem 95CE

The probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Explanation of Solution

Calculation:

The formula for finding the probability P(A− and F−) is,

P(A− and F−)=Frequency for the class A− and F−Total frequencies in the distribution

Substitute 7 for ‘Frequency for the class A– and F–’ and 34 for ‘Total frequencies in the distribution’,

P(A− and F−)=734=0.2059

Therefore, the probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 5, Problem 95CE

i.

To determine

Calculate probability P(F−) and explain its meaning.

i.

Expert Solution

Answer to Problem 95CE

The probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Explanation of Solution

Calculation:

The given table shows that frequencies of the actual and predicted interest rate movements.

The given contingency table is,

	Actual Change
Forecast Change	Decline (A–)	Rise (A+)	Row Total
Decline (F–)	7	12	19
Rise (F+)	9	6	15
Column Total	16	18	34

The formula for finding the probability P(F−) is,

P(F−)=Frequency for the class F−Total frequencies in the distribution.

Substitute 19 for ‘Frequency for the class F–’ and 34 for ‘Total frequencies in the distribution’

P(F−)=1934=0.5588

Therefore, the probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

ii.

To determine

Calculate probability P(A+) and explain its meaning.

ii.

Expert Solution

Answer to Problem 95CE

The probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+) is,

P(A+)=Frequency for the class A+Total frequencies in the distribution

Substitute 18 for ‘Frequency for the class A+’ and 34 for ‘Total frequencies in the distribution’

P(A+)=1834=0.5294

Therefore, the probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

iii.

To determine

Calculate probability P(A−|F−) and explain its meaning.

iii.

Expert Solution

Answer to Problem 95CE

The probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Explanation of Solution

Calculation:

The formula for finding the probability P(A−|F−) is,

P(A−|F−)=Frequency for the class A− and F−Frequency for the class F−

Substitute 7 for ‘Frequency for the class A– and F–’ and 19 for ‘Frequency for the class F–’,

P(A−|F−)=719=0.3684

Therefore, the probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

iv.

To determine

Calculate probability P(A+|F+) and explain its meaning.

iv.

Expert Solution

Answer to Problem 95CE

The probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+|F+) is,

P(A+|F+)=Frequency for the class A+ and F+Frequency for the class F+

Substitute 6 for ‘Frequency for the class A+ and F+’ and 15 for ‘Frequency for the class F+’,

P(A+|F+)=615=0.4

Therefore, the probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

v.

To determine

Calculate probability P(A+ and F+) and explain its meaning.

v.

Expert Solution

Answer to Problem 95CE

The probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+ and F+) is,

P(A+ and F+)=Frequency for the class A+ and F+Total frequencies in the distribution

Substitute 6 for ‘Frequency for the class A+ and F+’ and 34 for ‘Total frequencies in the distribution’,

P(A+ and F+)=634=0.1765

Therefore, the probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

vi.

To determine

Calculate probability P(A− and F−) and explain its meaning.

vi.

Expert Solution

Answer to Problem 95CE

The probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Explanation of Solution

Calculation:

The formula for finding the probability P(A− and F−) is,

P(A− and F−)=Frequency for the class A− and F−Total frequencies in the distribution

Substitute 7 for ‘Frequency for the class A– and F–’ and 34 for ‘Total frequencies in the distribution’,

P(A− and F−)=734=0.2059

Therefore, the probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 5, Problem 95CE

i.

To determine

Calculate probability P(F−) and explain its meaning.

i.

Expert Solution

Answer to Problem 95CE

The probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Explanation of Solution

Calculation:

The given table shows that frequencies of the actual and predicted interest rate movements.

The given contingency table is,

	Actual Change
Forecast Change	Decline (A–)	Rise (A+)	Row Total
Decline (F–)	7	12	19
Rise (F+)	9	6	15
Column Total	16	18	34

The formula for finding the probability P(F−) is,

P(F−)=Frequency for the class F−Total frequencies in the distribution.

Substitute 19 for ‘Frequency for the class F–’ and 34 for ‘Total frequencies in the distribution’

P(F−)=1934=0.5588

Therefore, the probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

ii.

To determine

Calculate probability P(A+) and explain its meaning.

ii.

Expert Solution

Answer to Problem 95CE

The probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+) is,

P(A+)=Frequency for the class A+Total frequencies in the distribution

Substitute 18 for ‘Frequency for the class A+’ and 34 for ‘Total frequencies in the distribution’

P(A+)=1834=0.5294

Therefore, the probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

iii.

To determine

Calculate probability P(A−|F−) and explain its meaning.

iii.

Expert Solution

Answer to Problem 95CE

The probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Explanation of Solution

Calculation:

The formula for finding the probability P(A−|F−) is,

P(A−|F−)=Frequency for the class A− and F−Frequency for the class F−

Substitute 7 for ‘Frequency for the class A– and F–’ and 19 for ‘Frequency for the class F–’,

P(A−|F−)=719=0.3684

Therefore, the probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

iv.

To determine

Calculate probability P(A+|F+) and explain its meaning.

iv.

Expert Solution

Answer to Problem 95CE

The probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+|F+) is,

P(A+|F+)=Frequency for the class A+ and F+Frequency for the class F+

Substitute 6 for ‘Frequency for the class A+ and F+’ and 15 for ‘Frequency for the class F+’,

P(A+|F+)=615=0.4

Therefore, the probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

v.

To determine

Calculate probability P(A+ and F+) and explain its meaning.

v.

Expert Solution

Answer to Problem 95CE

The probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+ and F+) is,

P(A+ and F+)=Frequency for the class A+ and F+Total frequencies in the distribution

Substitute 6 for ‘Frequency for the class A+ and F+’ and 34 for ‘Total frequencies in the distribution’,

P(A+ and F+)=634=0.1765

Therefore, the probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

vi.

To determine

Calculate probability P(A− and F−) and explain its meaning.

vi.

Expert Solution

Answer to Problem 95CE

The probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Explanation of Solution

Calculation:

The formula for finding the probability P(A− and F−) is,

P(A− and F−)=Frequency for the class A− and F−Total frequencies in the distribution

Substitute 7 for ‘Frequency for the class A– and F–’ and 34 for ‘Total frequencies in the distribution’,

P(A− and F−)=734=0.2059

Therefore, the probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 5, Problem 95CE

i.

To determine

Calculate probability P(F−) and explain its meaning.

i.

Expert Solution

Answer to Problem 95CE

The probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Explanation of Solution

Calculation:

The given table shows that frequencies of the actual and predicted interest rate movements.

The given contingency table is,

	Actual Change
Forecast Change	Decline (A–)	Rise (A+)	Row Total
Decline (F–)	7	12	19
Rise (F+)	9	6	15
Column Total	16	18	34

The formula for finding the probability P(F−) is,

P(F−)=Frequency for the class F−Total frequencies in the distribution.

Substitute 19 for ‘Frequency for the class F–’ and 34 for ‘Total frequencies in the distribution’

P(F−)=1934=0.5588

Therefore, the probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

ii.

To determine

Calculate probability P(A+) and explain its meaning.

ii.

Expert Solution

Answer to Problem 95CE

The probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+) is,

P(A+)=Frequency for the class A+Total frequencies in the distribution

Substitute 18 for ‘Frequency for the class A+’ and 34 for ‘Total frequencies in the distribution’

P(A+)=1834=0.5294

Therefore, the probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

iii.

To determine

Calculate probability P(A−|F−) and explain its meaning.

iii.

Expert Solution

Answer to Problem 95CE

The probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Explanation of Solution

Calculation:

The formula for finding the probability P(A−|F−) is,

P(A−|F−)=Frequency for the class A− and F−Frequency for the class F−

Substitute 7 for ‘Frequency for the class A– and F–’ and 19 for ‘Frequency for the class F–’,

P(A−|F−)=719=0.3684

Therefore, the probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

iv.

To determine

Calculate probability P(A+|F+) and explain its meaning.

iv.

Expert Solution

Answer to Problem 95CE

The probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+|F+) is,

P(A+|F+)=Frequency for the class A+ and F+Frequency for the class F+

Substitute 6 for ‘Frequency for the class A+ and F+’ and 15 for ‘Frequency for the class F+’,

P(A+|F+)=615=0.4

Therefore, the probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

v.

To determine

Calculate probability P(A+ and F+) and explain its meaning.

v.

Expert Solution

Answer to Problem 95CE

The probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+ and F+) is,

P(A+ and F+)=Frequency for the class A+ and F+Total frequencies in the distribution

Substitute 6 for ‘Frequency for the class A+ and F+’ and 34 for ‘Total frequencies in the distribution’,

P(A+ and F+)=634=0.1765

Therefore, the probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

vi.

To determine

Calculate probability P(A− and F−) and explain its meaning.

vi.

Expert Solution

Answer to Problem 95CE

The probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Explanation of Solution

Calculation:

The formula for finding the probability P(A− and F−) is,

P(A− and F−)=Frequency for the class A− and F−Total frequencies in the distribution

Substitute 7 for ‘Frequency for the class A– and F–’ and 34 for ‘Total frequencies in the distribution’,

P(A− and F−)=734=0.2059

Therefore, the probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Answer 6

Chapter 5, Problem 95CE

i.

To determine

Calculate probability P(F−) and explain its meaning.

i.

Expert Solution

Answer to Problem 95CE

The probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Explanation of Solution

Calculation:

The given table shows that frequencies of the actual and predicted interest rate movements.

The given contingency table is,

	Actual Change
Forecast Change	Decline (A–)	Rise (A+)	Row Total
Decline (F–)	7	12	19
Rise (F+)	9	6	15
Column Total	16	18	34

The formula for finding the probability P(F−) is,

P(F−)=Frequency for the class F−Total frequencies in the distribution.

Substitute 19 for ‘Frequency for the class F–’ and 34 for ‘Total frequencies in the distribution’

P(F−)=1934=0.5588

Therefore, the probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Answer 7

Chapter 5, Problem 95CE

i.

To determine

Calculate probability P(F−) and explain its meaning.

Answer 8

i.

Expert Solution

Answer to Problem 95CE

The probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Answer 9

i.

Expert Solution

Answer 10

i.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Calculation:

The given table shows that frequencies of the actual and predicted interest rate movements.

The given contingency table is,

	Actual Change
Forecast Change	Decline (A–)	Rise (A+)	Row Total
Decline (F–)	7	12	19
Rise (F+)	9	6	15
Column Total	16	18	34

The formula for finding the probability P(F−) is,

P(F−)=Frequency for the class F−Total frequencies in the distribution.

Substitute 19 for ‘Frequency for the class F–’ and 34 for ‘Total frequencies in the distribution’

P(F−)=1934=0.5588

Therefore, the probability P(F−) is 0.5588 and the meaning is the probability of forecasts predicted a decline in interest rates is 0.5588.

Answer 13

ii.

To determine

Calculate probability P(A+) and explain its meaning.

ii.

Expert Solution

Answer to Problem 95CE

The probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+) is,

P(A+)=Frequency for the class A+Total frequencies in the distribution

Substitute 18 for ‘Frequency for the class A+’ and 34 for ‘Total frequencies in the distribution’

P(A+)=1834=0.5294

Therefore, the probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Answer 14

ii.

To determine

Calculate probability P(A+) and explain its meaning.

Answer 15

ii.

Expert Solution

Answer to Problem 95CE

The probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Answer 16

ii.

Expert Solution

Answer 17

ii.

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Calculation:

The formula for finding the probability P(A+) is,

P(A+)=Frequency for the class A+Total frequencies in the distribution

Substitute 18 for ‘Frequency for the class A+’ and 34 for ‘Total frequencies in the distribution’

P(A+)=1834=0.5294

Therefore, the probability P(A+) is 0.5294 and the meaning is the probability of rise in interest rates is 0.5294.

Answer 20

iii.

To determine

Calculate probability P(A−|F−) and explain its meaning.

iii.

Expert Solution

Answer to Problem 95CE

The probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Explanation of Solution

Calculation:

The formula for finding the probability P(A−|F−) is,

P(A−|F−)=Frequency for the class A− and F−Frequency for the class F−

Substitute 7 for ‘Frequency for the class A– and F–’ and 19 for ‘Frequency for the class F–’,

P(A−|F−)=719=0.3684

Therefore, the probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Answer 21

iii.

To determine

Calculate probability P(A−|F−) and explain its meaning.

Answer 22

iii.

Expert Solution

Answer to Problem 95CE

The probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Answer 23

iii.

Expert Solution

Answer 24

iii.

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Calculation:

The formula for finding the probability P(A−|F−) is,

P(A−|F−)=Frequency for the class A− and F−Frequency for the class F−

Substitute 7 for ‘Frequency for the class A– and F–’ and 19 for ‘Frequency for the class F–’,

P(A−|F−)=719=0.3684

Therefore, the probability P(A−|F−) is 0.3684 and the meaning is the probability of actual decline given that the forecasters predicted a decline in interest rates is 0.3684.

Answer 27

iv.

To determine

Calculate probability P(A+|F+) and explain its meaning.

iv.

Expert Solution

Answer to Problem 95CE

The probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+|F+) is,

P(A+|F+)=Frequency for the class A+ and F+Frequency for the class F+

Substitute 6 for ‘Frequency for the class A+ and F+’ and 15 for ‘Frequency for the class F+’,

P(A+|F+)=615=0.4

Therefore, the probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Answer 28

iv.

To determine

Calculate probability P(A+|F+) and explain its meaning.

Answer 29

iv.

Expert Solution

Answer to Problem 95CE

The probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Answer 30

iv.

Expert Solution

Answer 31

iv.

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Calculation:

The formula for finding the probability P(A+|F+) is,

P(A+|F+)=Frequency for the class A+ and F+Frequency for the class F+

Substitute 6 for ‘Frequency for the class A+ and F+’ and 15 for ‘Frequency for the class F+’,

P(A+|F+)=615=0.4

Therefore, the probability P(A+|F+) is 0.4 and the meaning is the probability of actual increase given that the forecasters predicted an increase in interest rates is 0.4.

Answer 34

v.

To determine

Calculate probability P(A+ and F+) and explain its meaning.

v.

Expert Solution

Answer to Problem 95CE

The probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Explanation of Solution

Calculation:

The formula for finding the probability P(A+ and F+) is,

P(A+ and F+)=Frequency for the class A+ and F+Total frequencies in the distribution

Substitute 6 for ‘Frequency for the class A+ and F+’ and 34 for ‘Total frequencies in the distribution’,

P(A+ and F+)=634=0.1765

Therefore, the probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Answer 35

v.

To determine

Calculate probability P(A+ and F+) and explain its meaning.

Answer 36

v.

Expert Solution

Answer to Problem 95CE

The probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Answer 37

v.

Expert Solution

Answer 38

v.

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

Calculation:

The formula for finding the probability P(A+ and F+) is,

P(A+ and F+)=Frequency for the class A+ and F+Total frequencies in the distribution

Substitute 6 for ‘Frequency for the class A+ and F+’ and 34 for ‘Total frequencies in the distribution’,

P(A+ and F+)=634=0.1765

Therefore, the probability P(A+ and F+) is 0.1765 and the meaning is the probability of both forecasted increase and actual increase in interest rates in a given year is 0.1765.

Answer 41

vi.

To determine

Calculate probability P(A− and F−) and explain its meaning.

vi.

Expert Solution

Answer to Problem 95CE

The probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Explanation of Solution

Calculation:

The formula for finding the probability P(A− and F−) is,

P(A− and F−)=Frequency for the class A− and F−Total frequencies in the distribution

Substitute 7 for ‘Frequency for the class A– and F–’ and 34 for ‘Total frequencies in the distribution’,

P(A− and F−)=734=0.2059

Therefore, the probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Answer 42

vi.

To determine

Calculate probability P(A− and F−) and explain its meaning.

Answer 43

vi.

Expert Solution

Answer to Problem 95CE

The probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.

Answer 44

vi.

Expert Solution

Answer 45

vi.

Expert Solution

Answer 46

Expert Solution

Answer 47

Explanation of Solution

Calculation:

The formula for finding the probability P(A− and F−) is,

P(A− and F−)=Frequency for the class A− and F−Total frequencies in the distribution

Substitute 7 for ‘Frequency for the class A– and F–’ and 34 for ‘Total frequencies in the distribution’,

P(A− and F−)=734=0.2059

Therefore, the probability P(A− and F−) is 0.2059 and the meaning is the probability of both forecasted decline and actual decline in interest rates in a given year is 0.2059.