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	229		217
No Preference	23		23
Faster	88		50

a. Is the preferred pace of life independent of gender? Using a .05 level of significance, what is the -value?

Compute the value of the  χ² test statistic (to 3 decimals).

 χ²= ??

The p-value = ??

What is your conclusion?

(Cannot conclude/Conclude) that the preferred pace of life is not independent of gender.

b. What are the percentage responses for each gender (to 1 decimal)?

	Gender
Preferred Pace of Life	Male	Female
Slower
No Preference
Faster

Discuss any differences between the preferences of men and women.

(Men only/Women only/Both men and women) prefer a slower pace of life. Women have a higher preference for a (slower/faster) pace of life, while men have a higher preference for a (slower/faster) pace of life.

Answer 1

a) Applying chi square test:

Expected	Ei=row total*column total/grand total	Male	Female	Total
	Slower	240.70	205.30	446
	No preference	24.83	21.17	46
	Faster	74.48	63.52	138
	total	340	290	630
chi square    χ2	=(Oi-Ei)2/Ei	Male	Female	Total
	Slower	0.569	0.667	1.235
	No preference	0.134	0.157	0.292
	Faster	2.456	2.879	5.335
	total	3.159	3.703	6.8616

test statistic X² =6.862

p value =0.0324

Conclude that the preferred pace of life is not independent of gender.

b)

Preferred Pace of Life	Male	Female
Slower	67.4%	74.8%
No Preference	6.8%	7.9%
Faster	25.9%	17.2%

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 faster pace of life.