Question

III. A study looked at n = 238 adolescents, all free of severe illness.²² Subjects wore a wrist actigraph, which allowed the researchers to estimate sleep patterns. Those subjects classified as having low sleep efficiency had an average systolic blood pressure that was 5.8 millimeters of mercury (mm Hg) higher than that of other adolescents. The standard deviation of the population difference is 21.6 mm Hg. Based on these results, test whether this difference is significant at the 0.01 level. State a conclusion.

Answer 1

Null hypothesis:- mean difference is not significant

Alternate hypothesis:- mean difference is significant (testing claim)

we have sample size n = 238, mean difference = 5.8 and standard deviation for difference = 21.6

Formula test statistics is given as

setting the values, we get

this gives us

degree of freedom = n-1 = 238-1 = 237

Using excel function tdist or t distribution with t value 4.413 and df = 237 for one tailed hypothesis, we get

p value = 0.000024

So, it is clear that the p value is less than 0.01 significance level, rejecting the null hypothesis as result is significant.

Thus, we can conclude that at 0.01 level of significance, the difference between mean is significant.

We have sufficient evidecen to conclude that the mean differene is significant at 0.01 level of significance.