Question

The average number of hours slept per week for college seniors is believed to be about 60 hours. A researcher asks 10 random seniors at a University how many hours they sleep per week. Based on the following results, should the researcher conclude that college seniors do or do not sleep an average of 60 hours per week?

Data (average number of hours slept per week): 70; 45; 55; 60; 65; 55; 55; 60; 50; 55

A: What is the null hypothesis for this study?

B: What is the alternative hypothesis for this study?

C: What is the standard deviation of this sample?

D: How many degrees of freedom are there for this data?

E: For an alpha level of 0.05 (two-tailed), what is the critical t-value?

F: Should the researcher accept or reject the null hypothesis?

Answer 1

A.

Null hypothesis H0: Average number of hours slept per week for college seniors is 60 hours.

B.

Alternative hypothesis H0: Average number of hours slept per week for college seniors is not 60 hours.

C.

From the data,

Sample mean, = 57

Sample standard deviation, sd = 7.15

D.

Degree of freedom = n-1 = 10-1 = 9

E.

For alpha level of 0.05 (two-tailed), and df = 9, the critical t-value is  2.26

We reject the null hypothesis H0, if t < -2.26 or t > 2.26

F.

Standard error of mean = sd / = 7.15 / =  2.26

Test statistic, t = ( - ) / SE = (57 - 60) / 2.26 = -1.33

Since the test statistic does not fall in the rejection region, we fail to reject null hypothesis H0 and conclude that there is no strong evidence to reject the belief that the average number of hours slept per week for college seniors is 60 hours.

The researcher should accept the null hypothesis.