7. Sampling Distributions & Confidence Intervals: Mean

Mint Specs Listed below are weights (grams) from a simple random sample of pennies produced after 1983 (from Data Set 40 “Coin Weights” in Appendix B).

b. How does the result compare to the confidence interval found in Exercise 14 in Section 7-3?

Good Sample? An economist is investigating the incomes of college students. Because she lives in Maine, she obtains sample data from that state. Is the resulting mean income of college students a good estimator of the mean income of college students in the United States? Why or why not?

Critical Values Sir R. A. Fisher, a famous statistician, showed that the critical values of a chi-square distribution can be approximated by the standard normal distribution

χ²_k = [(z_k + √(2v – 1)) / 2]²

where v is the degrees of freedom and z_k is the z-score such that the area under the standard normal curve to the right of z_k is k. Use Fisher’s approximation to find χ²_0.975 and χ²_0.025 with 100 degrees of freedom. Compare the results with those found in Table VIII.

Which of the following is the best interpretation of the power of a significance test?

In the context of hypothesis testing, if the significance level is set at $10\%$, what does this significance level represent?

What is a confidence interval? Choose the best description.

Which of the following best describes a $95\%$ confidence interval for a population mean?

For a 90% confidence interval for the population mean, what is the value of $z_{\frac{\alpha }{2}}$?

In the context of hypothesis testing, what is the impact of increasing the sample size on the $p$-value, assuming the effect size remains constant?

In which of the following situations is it appropriate to use the confidence interval formula for a proportion ($p$)?

Which of the following statements is correct concerning statistical sampling in tests of controls?

If the confidence level is increased from $90\%$ to $99\%$, what happens to the width of the confidence interval for a population mean (assuming all other factors remain constant)?

Identifying data that are out of the ordinary is part of which step of the data cleaning process?

Which of the following calculations is not derived from the $confidence interval$?

Which of the following is not a time-series model?