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The average student loan debt of a U.S. college student at the end of four years of college is estimated to be about $22,500. You take a simple random sample of 122 college students in the state of Wyoming (who are at the end of their fourth year) and find the mean debt is $21,200 with a standard deviation of $1,990.
(a) Calculate the 90% confidence interval for the mean student debt of all fourth-year Wyoming college students, and interpret the result.
(b) Calculate the 95% confidence interval for the mean student debt of all fourth-year Wyoming college students, and interpret the result.
(c) Repeat part (b) but assume that the population standard deviation is known to be $2,020.
(d) If the margin of error is to be reduced to $200 (i.e. the population mean is expected to be within $200 of the sample mean), and if the confidence level is kept at 99% with the population standard deviation of $2,020, what should be the sample size?
(e) You need to test whether the mean debt of all fourth-year Wyoming college students differ significantly from the national average given above.
1) State the claim (or research question).
2) State the hypotheses.
3) Using 5% significance level, specify the critical values, and identify rejection and non-rejection regions.
4) Calculate the test statistic (show the calculations). Use the sample standard deviation given at the beginning of the problem.
5) Statethe decision, and explain what it means (look at the hypotheses).
6) Calculate (or estimate) the p-value.
7) Interpret the p-value