Question

Med Student Sleep Average (Raw Data, Software Required):
Here we consider a small study on the sleep habits of med students and non-med students. The study consists of the hours of sleep per night obtained from 30 non-med students and 25 med students. The sample data is given in the table below. Test the claim that, on average, the mean hours of sleep for all med students is different from that for non-med students. Test this claim at the 0.01 significance level.

(a) The claim states there is a difference between population means (μ1 − μ2 ≠ 0). What type of test is this? This is a two-tailed test. This is a right-tailed test.    This is a left-tailed test. (b) Use software to calculate the test statistic. Do not 'pool' the variance. This means you do not assume equal variances. Round your answer to 2 decimal places. t = (c) Use software to get the P-value of the test statistic. Round to 4 decimal places. P-value = (d) What is the conclusion regarding the null hypothesis? reject H0 fail to reject H0     (e) Choose the appropriate concluding statement. The data supports the claim that, on average, the mean hours of sleep for all med students is different from that for non-med students. There is not enough data to support the claim that, on average, the mean hours of sleep for all med students is different from that for non-med students.     We reject the claim that, on average, the mean hours of sleep for all med students is different from that for non-med students. We have proven that, on average, the mean hours of sleep for all med students is different from that for non-med students.

Non-Med (x1) Med (x2) 6.3 5.6 8.7 8.1 5.0 4.5 5.1 4.5 4.0 3.4 6.3 5.7 6.8 6.3 7.9 7.2 6.7 6.0 5.1 4.5 5.2 4.5 4.8 4.3 5.7 5.1 6.5 5.8 4.6 3.9 8.0 7.3 3.1 2.6 6.1 5.4 4.8 4.2 5.7 5.1 7.1 6.4 7.7 7.1 5.8 5.2 5.9 5.4 7.8 7.2 6.8 9.4 9.5 7.8 6.3

Answer 1

(a) This is a two-tailed test.

In order to derive the results, we make use of MS-Excel & the steps are as follows :

Step 1 : Enter the data in excel.
Step 2 : Select the "t-Test: Two-Sample Assuming Unequal Variances" function from the data analysis package available under the data tab of MS-Excel.
Step 3 : Enter the range of Non-med in the first cell & the range of Med in the second cell,
Step 4 : Change the level of significance(l.o.s.) from 0.05 to 0.01.
Step 5 : Click ok & thus, following results are obtained :

t-Test: Two-Sample Assuming Unequal Variances
	Non-Med (x1)	Med (x2)
Mean	6.35	5.412
Variance	2.367413793	1.7886
Observations	30	25
Hypothesized Mean Difference	0
df	53
t Stat	2.418218252
P(T<=t) one-tail	0.0095329
t Critical one-tail	2.398789836
P(T<=t) two-tail	0.019065799
t Critical two-tail	2.671822636

(b) t stat = 2.42

(c) p-value = 0.0191

(d) Since t stat < t Critical two-tail & p-value > 0.01, we fail to reject Ho at 1% l.o.s.

(e) There is not enough data to support the claim that, on average, the mean hours of sleep for all med students is different from that for non-med students.   

Hope this answers your query!