Question

A researcher is interested in whether college students get enough sleep. She suspects
that they get less than 8 hours of sleep on average. The sample mean (x ̄) for 65 students
was 7.08 hours. The standard deviation of number of hours students slept 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 significance level of .05, write a one or
two sentence conclusion in context of the problem.

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

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

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

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

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

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

Answer 1

( c )

we are 95 % confident that the true mean   college students get   enough sleep lies between  6.634 hours and 7.526 hours