Question

A Pew Research Center survey asked respondents if they would rather live in a place with a slower pace of life or a place with a faster pace of life. The survey also asked the respondent's gender. Consider the following sample data. Gender Preferred Pace of Life Male Female Slower 233 218 No Preference 17 22 Faster 90 50 a. Is the preferred pace of life independent of gender? Using a .05 level of significance, what is the p-value? f the x test statistic (to 3 decimals). Compute the value The n-value is-Select vour answer - What is your conclusion? that the preferred pace of life not independent of gender. Select your answer- b. What are the percentage responses for each gender (to 1 decimal)? Gender Male Female Preferred Pace of Life Slower No Preference Faster Discuss any differences between the preferences of men and women. prefer a slower pace of life. Women have a higher preference for a pace of life. - Select your answer- pace of life, while men have a higher preference for a Select your answer- - Select your answer-

Answer 1

Observed Frequencies	Male	Female	Total
Slower	233	218	451
No Preference	17	22	39
Faster	90	50	140
Total	340	290	630

Expected Frequencies	Male	Female	Total
Slower	(451 * 340)/630 = 243.3968	(451 * 290)/630 = 207.6032	451
No Preference	(39 * 340)/630 = 21.04762	(39 * 290)/630 = 17.95238	39
Faster	(140 * 340)/630 = 75.55556	(140 * 290)/630 = 64.44444	140
Total	340	290	630

= O- E/E 2

= (233 - 243.3968)² / 243.3968 + (218 - 207.6032)² / 207.6032 + (17 - 21.04762)² / 21.04762 + (22 - 17.95238)² / 17.95238 + (90 - 75.55556)² / 75.55556 + (50 - 64.44444)² / 64.44444

= 8.655

Degree of freedom = (r - 1) * (c - 1) = (3 - 1) * (2 - 1) = 2

P-value = P($\chi^2$ > 8.655, df = 2) = 0.0132

Since p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that

There is significant evidence that the preferred pace of life is not independent of gender.

b.

The percentage responses are get by dividing each cell data by 630 and then multiply by 100 to get the percentages.

Percentage responses	Male	Female
Slower	37.0	34.6
No Preference	2.7	3.5
Faster	14.3	7.9

Both men and women prefer a slower pace of life. Women have a higher preference for a slower pace of life, while men have a higher preference for a slower pace of life.