Question

Here we consider the sleep habits of med students versus non-med students. The study consists of the hours of sleep per day obtained from 25 med students and 28 non-med students. The summarized data is given in the table. Here, x¯ is the mean hours of sleep per day from each sample. The degrees of freedom (d.f.) is given to save calculation time if you are not using software.

Student Type	n	x¯	s2	s
Med (?1x1)	25	5.6	0.8281	0.91
Non-Med (?2x2)	28	6.2	1.7161	1.31
degrees of freedom: d.f. = 48

Test the claim that the mean hours of sleep for med and non-med students is different. Use a 0.05 significance level.

(a) Find the test statistic.

(b) Find the positive critical value.

(c) Find the negative critical value.

(d) Is there sufficient data to support the claim?
Yes
No

Test the claim that, on average, med students get less sleep than non-med students. Use a 0.05 significance level.

(e) Find the critical value.

(f) Is there sufficient data to support the claim?
Yes
No

Answer 1

Student Type	n		s2	s
Med (?1)	25	5.6	0.8281	0.91
Non-Med (?2)	28	6.2	1.7161	1.31
degrees of freedom: d.f. = 48

Null and alternative hypothesis:

Significance level, = 0.05

(a) Test statistic:

df = 48

(b) positive critical value = T.INV.2T(0.05, 48) = 2.0106

(c) negative critical value. = -T.INV.2T(0.05, 48) = -2.0106

(d) As t = -1.9527 > -2.0106, we fail to reject the null hypothesis.

No, there is not sufficient evidence.

Null and alternative hypothesis:

(e) critical value for left tailed test = T.INV(0.05, 48) = -1.677

(f) As t = -1.9527 < -1.677, we reject the null hypothesis.

Yes, there is sufficient evidence.