A sociologist believes that for people under the age of 30, men sleep longer per

Question

A sociologist believes that for people under the age of 30, men sleep longer per night on the weekend than women. 24 people were surveyed. Test at alpha = 5%. The following summary statistics were determined from the sample.

MEAN HOURS:
Men: 11.45
Women: 10.18

STANDARD DEV. HOURS:
Men: 1.95
Women: 2.81

n:
Men: 11
Women: 13

a) State the Null and Alternate Hypothesis in symbols and in words.

b) Calculate the expected results for the hypothesis test sampling distribution, assuming the Null Hypothesis is true. (i.e., name and graph of the sampling distribution, mean and standard error)

c) Identify the standard distribution that best approximates the sampling distribution.

d) Formulate the decision rule (you can use either critical test scores or p - values)

e) Determine the statistical sample results, i.e., the differences between the sample means, the pooled standard deviations, the standard error, the test statistic and p - value.

f) Determine the conclusion in terms of the Null and Alternate Hypotheses. Do the sample results indicate that the sociologist’s claim is supported at alpha = 5%?

Explanation / Answer

(a) Null Hypothesis : H0 : Time spent in sleeping in nights on weekends is equal for men and women. men = women

ALternative Hypothesis : Ha : Time spent in sleeping in nights on weekends is higher for men than women. men = women

(b) Assuming the null hypothesis is true, it will be t distribution and it is expected that there will no difference in men and women sleeping time in weekends. Here mean difference is (11.45 - 10.18 = 1.27 hours) and standard error is the pooled standard deviation which we will calculate.

(c) T- distribution will be the best approximated the sampling distribution.

(d) Decision rule here is that the p - value must be less than 0.05 to reject the null hypothesis and the test is uni- directional.

(E) Test statistics

Pooled standard deviation sp = sqrt [(n1 -1) s12 + (n2 -1)s2 2 / n1 + n2 -2)]

sp = sqrt [ (10 * 1.952 + 12 * 2.812 )/ 22] = 2.4567

standard error of difference se0 = sp * sqrt [1/n1 + 1/n2 ] = 2.4567 * sqrt [1/11 + 1/13] = 1.00

Test statistic

t = (xwomen - xmen)/ (seo ) = (11.45 - 10.18)/ 1.00 = 1.27

Here p - value is 0.1087

so which is greater than 0.05 . so we cannot reject the null hypothesis.

(f) We cannot reject the null hypthesis and sample results indicate that the sociologist claim's is rejected that Time spent in sleeping in nights on weekends is higher for men than women, is false.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.