Concept explainers
Mortgage rates: Following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon. Georgia on June 20. 2013. Is reasonable to assume that the population is approximately normal.
- Find the sample standard deviation s.
- Construct a 95% confidence interval for population standard deviation
- Base on the confidence interval. Is it reasonable to believe that the population standard deviation is greater than 0.5? Explain.
(a)
The sample standard deviation
Answer to Problem 18E
The sample standard deviation is
Explanation of Solution
Given information:
Following are interest rates (annual percentage rates) for a
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It is assumed that the population is normally distributed.
Calculation:
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By using MINITAB sample standard deviation is calculated with the help of following steps :
1) Import the data.
2) Select the Stat and choose the Basic Statistics option.
3) Select the
4) Select Confidence level
5) Click ok.
Test and
for One Variance: Rate
Statistics
From the MIN TAB output, the sample standard deviation is
(b)
The
Answer to Problem 18E
A
Explanation of Solution
Given information:
Following are interest rates (annual percentage rates) for a
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It is assumed that the population is normally distributed.
Calculation:
By using MINITAB a
confidence interval is calculated with the help of following steps :
1) Import the data.
2) Select the Stat and choose the Basic Statistics option.
3) Select the
4) Select Confidence level
5) Click ok.
Test and
for One Variance: Rate
Statistics
From the MINITAB output, a
(c)
Whether it is reasonable to believe that the population standarddeviation is greater than
Answer to Problem 18E
It is not reasonable to believe that the population standard deviation is greater than
Explanation of Solution
Given information:
Following are interest rates (annual percentage rates) for a
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It is assumed that the population is normally distributed.
Formula used:
Based on confidence interval, ¡t is reasonable to believe that the population standard deviation higher than
Calculation:
From part
Since the
Hence it is not reasonable to believe that the population standard deviation is greater than
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Chapter 8 Solutions
Elementary Statistics 2nd Edition
- 19. Let X be a non-negative random variable. Show that lim nE (IX >n)) = 0. E lim (x)-0. = >arrow_forward(c) Utilize Fubini's Theorem to demonstrate that E(X)= = (1- F(x))dx.arrow_forward(c) Describe the positive and negative parts of a random variable. How is the integral defined for a general random variable using these components?arrow_forward
- 26. (a) Provide an example where X, X but E(X,) does not converge to E(X).arrow_forward(b) Demonstrate that if X and Y are independent, then it follows that E(XY) E(X)E(Y);arrow_forward(d) Under what conditions do we say that a random variable X is integrable, specifically when (i) X is a non-negative random variable and (ii) when X is a general random variable?arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt