Revisiting drive-thru speaker clarity. In Exercise, you compared men's satisfaction with drive-thru speaker clarity with that of women using the two-sample t procedures that do not assume equal standard deviations. Compare the means using a significance test and find the 95% confidence interval for the difference using the pooled methods. How do the results compare with those you obtained in given Exercise?
Exercise
Drive-thru speaker clarity. QSRMagazine.com surveyed 689 adults on their drive-thru window experiences at quick-service restaurants.24 One question was "Thinking about your most recent drive-thru experience, please rate how satisfied you were with the clarity of communication through the speaker." Responses ranged from "Very Dissatisfied (1)" to "Very Satisfied (5)." The following table breaks down the responses according to gender:
|
|
Ratings
|
|
Gender
|
1
|
2
|
3
|
4
|
5
|
|
Female
|
5
|
44
|
48
|
183
|
188
|
|
Male
|
5
|
29
|
30
|
91
|
66
|
(a) Report the means and standard deviations of the rating for the male and female participants separately.
(b) Comment on the appropriateness of t procedures for these data.
(c) Test whether males and females are, on average, equally satisfied with speaker clarity. Use a two-sided alternative hypothesis and a significance level of 5%.
(d) Construct a 95% confidence interval for the difference in average satisfaction.
(e) Given the coarseness of the rating, the owner of the Sir Beef-a-lot chain considers only a difference in the means of at least 0.25 units as meaningful. Based on your results in parts (c) and (d), what would you tell this owner?