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 0.05 significance level.

Non-Med (x1)	Med (x2)
6.3	5.6
8.7	8.2
5.0	4.5
5.1	4.4
4.0	3.4
6.3	5.6
6.8	6.3
7.9	7.2
6.7	6.2
5.1	4.6
5.2	4.5
4.8	4.1
5.7	5.2
6.5	6.0
4.6	3.9
8.0	7.5
3.1	2.6
6.1	5.5
4.8	4.1
5.7	5.1
7.1	6.6
7.7	7.2
5.8	5.3
5.9	5.4
7.8	7.3
6.8
9.4
9.5
7.8
6.3

(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.

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.

(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.

Answer 1

By using Excel : THe output is ,

t-Test: Two-Sample Assuming Unequal Variances
	Variable 1	Variable 2
Mean	6.35	5.452
Variance	2.367413793	1.936766667
Observations	30	25
Hypothesized Mean Difference	0
df	53
t Stat	2.27080342
P(T<=t) one-tail	0.013624023
t Critical one-tail	1.674116237
P(T<=t) two-tail	0.027248046
t Critical two-tail	2.005745949

(a) Hypothesis : Vs

This test is two-tailed test.

(b) Test statistic=2.270803422.27

(c) P-value=0.0272480460.0272

(d) Decision : Here , P-value=0.0272<

Therefore , reject Ho

(e) Conclusion :  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.