
Concept explainers
(a)
Section 1:
To find: The difference of estimates for each subject.
(a)
Section 1:

Answer to Problem 40E
Solution: The table for difference of estimates is as follows,
Jocko |
Other |
Difference |
1410 |
1250 |
160 |
1550 |
1300 |
250 |
1250 |
1250 |
0 |
1300 |
1200 |
100 |
900 |
950 |
-50 |
1520 |
1575 |
-55 |
1750 |
1600 |
150 |
3600 |
3380 |
220 |
2250 |
2125 |
125 |
2840 |
2600 |
240 |
Explanation of Solution
Calculation: To calculate Difference follow the below mentioned steps in Minitab;
Step 1: Enter the variable name as ‘Jocko’ in column C1 and enter the provided data of ‘Jocko’s’. Enter the variable name as ‘Other’ in column C2 and enter the provided data of ‘Other’.
Step 2: Enter variable name as ‘Difference’ in column C3.
Step 3: Go to
Step 4: In the dialog box that appears, select ‘Difference’ in ‘Store result in variable’.
Step 5: Enter 'Jocko-Other' in ‘Expression’ and click ‘OK’.
From Minitab result, the table for weight change is as follows,
Jocko |
Other |
Difference |
1410 |
1250 |
160 |
1550 |
1300 |
250 |
1250 |
1250 |
0 |
1300 |
1200 |
100 |
900 |
950 |
-50 |
1520 |
1575 |
-55 |
1750 |
1600 |
150 |
3600 |
3380 |
220 |
2250 |
2125 |
125 |
2840 |
2600 |
240 |
Section 2:
To find: The
Section 2:

Answer to Problem 40E
Solution: The required mean is 114.0 and the standard deviation is 114.4
Explanation of Solution
Calculation: Follow the below mentioned steps in Minitab,
Step 1: Follow the step 1 to 5 performed in part (a).
Step 2: Go to
Step 3: In dialog box that appears select ‘Difference’ under the field marked as ‘Variables’. Then click on ‘Statistics’.
Step 4: In dialog box that appears select ‘None’ and then ‘Mean’. Finally, click ‘OK’ on both dialog boxes.
From Minitab result, the mean is 114.0 and the standard deviation is 114.4.
(b)
To test: The hypothesis that the estimates of the two garages do not differ significantly.
(b)

Answer to Problem 40E
Solution: The mean estimates for Jocko and Other differ significantly at 5% significance level.
Explanation of Solution
Calculation:
The null hypothesis is the hypothesis of no difference. If
The null hypothesis assumes that there is no significant difference and is formulated as,
And the alternative hypothesis assumes a significant change in the average estimates and is formulated as,
The formula of test statistic for paired t-test is as follows,
In the above formula,
The test statistic is calculated as,
The formula for degrees of freedom is as follows,
And it is calculated as,
To calculate the P-value follow the below mentioned steps in Minitab,
Step 1: Follow the step 1 to 5 performed in part (a).
Step 2: Go to
Step 3: In the dialogue box that appears, select samples in columns.
Step 4: Enter ‘Jocko’ under the field marked as ‘First sample’ and ‘Other’ under the field marked as ‘Second sample’.
Step 5: In the dialogue box that appears, Click on ‘Option’. Enter 95.0 in the field of Confidence interval, 0.0 in ‘Test mean’ and ‘not equal’ in ‘Alternative’.
From Minitab results, the P-value is 0.012.
Conclusion: Since, the P-value is 0.012 which is less than 0.05, the significance level. So the null hypothesis is rejected and it is concluded that the mean estimate for ‘Jocko’ is different from mean estimate for ‘Other’.
(c)
To find: The confidence interval.
(c)

Answer to Problem 40E
Solution: The required confidence interval is
Explanation of Solution
Calculation:
The confidence interval is an interval for which there is 95% chances that it contains the population parameter (population mean).
To calculate the confidence interval, follow the below mentioned steps in Minitab,
Step 1: Follow the step 1 to 5 performed in part (a).
Step 2: Go to
Step 3: In the dialogue box that appears, select samples in columns.
Step 4: Enter ‘Jocko’ under the field marked as ‘First sample’ and ‘Other’ under the field marked as ‘Second sample’.
Step 5: In the dialogue box that appears, Click on ‘Option’. Enter 95.0 in the field of Confidence interval, 0.0 in ‘Test mean’ and ‘not equal’ in ‘Alternative’.
From Minitab result, the confidence interval is
(d)
To explain: The repayment that is recommended to the insurance company seeks.
(d)

Answer to Problem 40E
Solution: The seeking repayment is recommended between $32.2 and $195.8.
Explanation of Solution
Want to see more full solutions like this?
Chapter 7 Solutions
Introduction to the Practice of Statistics
- Calculate the 90% confidence interval for the population mean difference using the data in the attached image. I need to see where I went wrong.arrow_forwardMicrosoft Excel snapshot for random sampling: Also note the formula used for the last column 02 x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51)) A B 1 No. States 2 1 ALABAMA Rand No. 0.925957526 3 2 ALASKA 0.372999976 4 3 ARIZONA 0.941323044 5 4 ARKANSAS 0.071266381 Random Sample CALIFORNIA NORTH CAROLINA ARKANSAS WASHINGTON G7 Microsoft Excel snapshot for systematic sampling: xfx INDEX(SD52:50551, F7) A B E F G 1 No. States Rand No. Random Sample population 50 2 1 ALABAMA 0.5296685 NEW HAMPSHIRE sample 10 3 2 ALASKA 0.4493186 OKLAHOMA k 5 4 3 ARIZONA 0.707914 KANSAS 5 4 ARKANSAS 0.4831379 NORTH DAKOTA 6 5 CALIFORNIA 0.7277162 INDIANA Random Sample Sample Name 7 6 COLORADO 0.5865002 MISSISSIPPI 8 7:ONNECTICU 0.7640596 ILLINOIS 9 8 DELAWARE 0.5783029 MISSOURI 525 10 15 INDIANA MARYLAND COLORADOarrow_forwardSuppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined. 1.What percent of the refunds are more than $3,500? 2. What percent of the refunds are more than $3500 but less than $3579? 3. What percent of the refunds are more than $3325 but less than $3579?arrow_forward
- A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts? 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the answer of the second part.) 2. Compute the probability of a value greater than 55.0. Use the same formula, x=55 and subtract the answer from 1. 3. Compute the probability of a value between 52.0 and 55.0. (The question requires finding probability value between 52 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 52, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…arrow_forwardIf a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by a step by step creating a chart. Clearly mark the range, identifying the…arrow_forwardClient 1 Weight before diet (pounds) Weight after diet (pounds) 128 120 2 131 123 3 140 141 4 178 170 5 121 118 6 136 136 7 118 121 8 136 127arrow_forward
- Client 1 Weight before diet (pounds) Weight after diet (pounds) 128 120 2 131 123 3 140 141 4 178 170 5 121 118 6 136 136 7 118 121 8 136 127 a) Determine the mean change in patient weight from before to after the diet (after – before). What is the 95% confidence interval of this mean difference?arrow_forwardIn order to find probability, you can use this formula in Microsoft Excel: The best way to understand and solve these problems is by first drawing a bell curve and marking key points such as x, the mean, and the areas of interest. Once marked on the bell curve, figure out what calculations are needed to find the area of interest. =NORM.DIST(x, Mean, Standard Dev., TRUE). When the question mentions “greater than” you may have to subtract your answer from 1. When the question mentions “between (two values)”, you need to do separate calculation for both values and then subtract their results to get the answer. 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…arrow_forwardIf a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by creating a chart. Clearly mark the range, identifying the lower and upper…arrow_forward
- Problem 1: The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of 40 per hour and a standard deviation of 3.00 per hour. What is the probability that the hourly pay of a randomly selected flight attendant is: Between the mean and $45 per hour? More than $45 per hour? Less than $32 per hour? Problem 2: The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. What is the area between 415 pounds and the mean of 400 pounds? What is the area between the mean and 395 pounds? What is the probability of randomly selecting a value less than 395 pounds? Problem 3: In New York State, the mean salary for high school teachers in 2022 was 81,410 with a standard deviation of 9,500. Only Alaska’s mean salary was higher. Assume New York’s state salaries follow a normal distribution. What percent of New York State high school teachers earn between 70,000 and 75,000? What percent of New York State high school…arrow_forwardPls help asaparrow_forwardSolve the following LP problem using the Extreme Point Theorem: Subject to: Maximize Z-6+4y 2+y≤8 2x + y ≤10 2,y20 Solve it using the graphical method. Guidelines for preparation for the teacher's questions: Understand the basics of Linear Programming (LP) 1. Know how to formulate an LP model. 2. Be able to identify decision variables, objective functions, and constraints. Be comfortable with graphical solutions 3. Know how to plot feasible regions and find extreme points. 4. Understand how constraints affect the solution space. Understand the Extreme Point Theorem 5. Know why solutions always occur at extreme points. 6. Be able to explain how optimization changes with different constraints. Think about real-world implications 7. Consider how removing or modifying constraints affects the solution. 8. Be prepared to explain why LP problems are used in business, economics, and operations research.arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman





