Question

Christine is the dean of students at a college. She is concerned about the amount of sleep students are getting. In particular, Christine is making an inquiry on whether students who are enrolled in the pre-med program are getting less sleep on average compared to students who are enrolled in other programs. The average amount of sleep per night for a random sample of 10 pre-med students and 10 students in other programs is recorded. Assume that the population standard deviation of hours of sleep per night is 0.6 hour for the pre-med students and 0.8 hour for the students in other programs, and that the number of hours of sleep per night for both groups of students is normally distributed. Let the pre-med students be the first sample, and let the other students be the second sample.

She conducts a two-mean hypothesis test at the 0.05 level of significance, to test if there is evidence that pre-med students are getting less sleep than students in other programs.

(a) H0:μ1=μ2; Ha:μ1<μ2, which is a left-tailed test.

Pre-Med Students	Other Students
5.3	6.3
6	5
5.1	6.8
5.6	7.1
5.1	6.3
4.9	6.5
5.9	6.1
5.2	5.3
5.7	6.8
6.1	5.8

The above table shows the average amount of sleep per night for a random sample of 10 pre-med students and 10 students in other programs.

(b) Use a TI-83, TI-83 Plus, or TI-84 calculator to test if the mean sleep for pre-med students is less than the mean sleep for other students. Identify the test statistic, z, and p-value from the calculator output. Round your test statistic to two decimal places and your p-value to three decimal places.

Answer 1

Solution:

(a)

H0:μ1=μ2; Ha:μ1<μ2, which is a left-tailed test.

(b)

The steps to be followed in the TI-84 calculator are:

Press STAT and then click on Edit

Enter the given data under L1 and L2

Then click on STAT and scroll right to TESTS.

Scroll down to 2-SampZTest...

Scroll right to Data and enter the values as:

Press calculate and the output is:

Therefore, the test statistic is: