Question

Med Student Sleep Average: 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 32 non-med students and 24 med students. The summarized data is given in the table below. Here,

x is the mean hours of sleep per night from each sample.

Necessary information:

	n	x	s2	s
Non−Med (x1)	32	6.3	1.9	1.38
Med (x2)	24	5.5	0.9	0.95

The Test: 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) Calculate the test statistic using software or the formula below

t =

(x1 − x2) − δ

s12 n1 + s22 n2

where δ is the hypothesized difference in means from the null hypothesis. Round your answer to 2 decimal places.
t =
To account for hand calculations -vs- software, your answer must be within 0.01 of the true answer.

(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.

Answer 1

Here we test the following hypothesis,

H₀ : the mean hours of sleep for all med students is same as that of non-med students i.e. v/s

H₁ : the mean hours of sleep for all med students is different from that for non-med students, i.e.  

(a) The following test is a two-tailed test.

(b) The test statistic is calculated using minitab software.

(Steps for calculation : Stat -- basic staistics -- two sample t -- choose summarized data -- input the data)

Thus the calculated t value = 2.57

(c) p value = 0.0130 ( calculated using minitab software)

(d) here since = level of significance

p value >

So, we fail to reject the null hypothesis

(e) The appropriate concluding statement is:

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.