Sleep by Med Students (Two-Tail & One-Tail Tests): Here we consider the sleep ha
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Question
Sleep by Med Students (Two-Tail & One-Tail Tests):
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 30 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.
Degrees of freedom: d.f. = 51
(a) The Two-Tailed Test: Test the claim that the mean hours of sleep for med and non-med students is different. Use a 0.05 significance level.
Student Type n x s2 s Med (x1) 25 5.7 0.9 0.95 Non-Med (x2) 30 6.3 1.9 1.38Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u1 - u2 = 0
Ha: u1 - u2 =/ 0
At level of significance = 0.05
As we can see, this is a two tailed test.
Calculating the means of each group,
X1 = 5.7
X2 = 6.3
Calculating the standard deviations of each group,
s1 = 0.95
s2 = 1.38
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 25
n2 = sample size of group 2 = 30
Also, sD = 0.315562989
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = -1.901363661
where uD = hypothesized difference = 0
df = 51
Now, the critical value for t is
tcrit = +/- 2.00758377
Also, using p values,
Pvalue = 0.062911275
As |t| < 2.008, and P > 0.05, WE FAIL TO REJECT THE NULL HYPOTHESIS.
Thus, there is no significant evidence that the mean hours of sleep for med and non-med students are different at 0.05 level. [CONCLUSION]
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