A researcher is interested in whether college students getenough sleep. She suspects
that they get less than 8 hours of sleep on average. The samplemean (x Ì„) for 65 students
was 7.08 hours. The standard deviation of number of hours studentsslept is s=1.8.
(a) Determine the null and alternative hypothesis for the test.What is the parameter
in this study?

(b) The p-value for the test is <0.0001. Using a significancelevel of .05, write a one or
two sentence conclusion in context of the problem.

(c) Calculate 95% confidence interval for μ, the mean number ofhours college students
sleep per night. Interpret the confidence interval. Be sure to usethe word mean or average in your interpretation and don’t forgetunits. If you are doing the calculations by hand use t* =1.998.

(d) Does your confidence interval support the results of thehypothesis test? Explain.

2. The College Board reported that the mean SAT score in 2009was 540 for all US High
School students that took the SAT. A teacher believes that the meanscore for his
students is greater than 540. He takes a random sample of 50 of hisstudents and
the sample mean score for the 25 students is 565 with a samplestandard deviation of
100. Does he have evidence that his students, on average, do betterthan the national
average?
(a) State the null and alternative hypotheses.

(b) The p-value for the above test was 0.1117. State aconclusion in context of the
problem. Use a significance level of 0.05.

(c) A 95% confidence interval for μ is (523.7,606.3). Interpretthe confidence interval
in context of the problem.

(d) Does your confidence interval support the results of thehypothesis test? Explain.