8. Sampling Distributions & Confidence Intervals: Proportion

Use a table to find or estimate ${\chi }^2$ such that:

$P(X^2>{\chi }^2)=0.010$ (Area to the right)

$df=50$

Use a table to find or estimate ${\chi }^2$ such that:

(Area to the left)

$df=50$

Find the left and right ${\chi }^2$-values for a 99% confidence interval with a sample size of 25.

Constructing Confidence Intervals In Exercises 13–24, assume the sample is from a normally distributed population and construct the indicated confidence intervals for (b) the population standard deviation σ. Interpret the results.

[APPLET] Earnings The annual earnings (in thousands of dollars) of 21 randomly selected level 1 computer hardware engineers are listed. Use a 99% level of confidence. (Adapted from Salary.com)

Performing a Two-Sample F-Test In Exercises 19–26, (a) identify the claim and state H0 and Ha, (b) find the critical value and identify the rejection region, (c) find the test statistic F, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed.

Heart Transplant Waiting Times The table at the left shows a sample of the waiting times (in days) for a heart transplant for two age groups. At α=0.05, can you conclude that the variances of the waiting times differ between the two age groups? (Adapted from Organ Procurement and Transplantation Network)

True or False: To construct a confidence interval about a population variance or standard deviation, either the population from which the sample is drawn must be normal, or the sample size must be large.

Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.

c = 0.98, n = 26

Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.

c = 0.80, n = 51

Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.

c = 0.99, n = 30

What happens to the shape of the chi-square distribution as the degrees of freedom increase?

Does a population have to be normally distributed to use the chi-square distribution?