Question

5) Media Research Inc. conducted a study of the radio listening habits of men and women. One facet of the study involved a participant’s listening time per day. a) State the Hypothesis to show the variation in the listening time depended on gender, i.e., is different for men and women b) Choose a level of a Use a= 0.10 for this problem. c) Media Research Inc. collected the number of hours spent listening to the radio for a random sample of 10 men and 11 women. The data appear in the Radio worksheet of the HW3 data workbook on Moodle. Collect data and calculate necessary statistics to test the hypothesis. d) Sketch the sampling distribution. Include the critical value and test statistic. e) Draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem. f) What is the p-value for the hypothesis test? g) Use Excel to perform the hypothesis test.

Men	Women
97	63
88	84
68	72
84	104
75	54
76	59
73	41
98	51
86	77
80	45
	80

Answer 1

Here we have data:

men	women
97	63
88	84
68	72
84	104
75	54
76	59
73	41
98	51
86	77
80	45
	80

Excel output:

t-Test: Two-Sample Assuming Unequal Variances
	Variable 1	Variable 2
Mean	82.5	66.3636364
Variance	100.0555556	361.254545
Observations	10	11
Hypothesized Mean Difference	0
df	15
t Stat	2.465165502
P(T<=t) one-tail	0.013123532
t Critical one-tail	1.340605608
P(T<=t) two-tail	0.026247064
t Critical two-tail	1.753050356

Hypotheses:

H_o: μ₁ = μ₂

H_a: μ₁≠μ₂

Test statistics:

t = 2.47

Critical value:

t-critical = 1.753

p-value = 2p(t>|2.47|) = 0.0262Here we have sufficient evidence to reject the null hypothesis, because t-observed value (2.47) is grater than t-critical value (1.753), and in the rejection region.

Conclusion: we can say that, the variation in the listening time depended on gender, i.e., is different for men and women.