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	232		218
No Preference	19		25
Faster	89		47

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

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

The -value is - Select your answer -between .01 and .025between .025 and .05between .05 and .10greater than .10less than .01Item 2

What is your conclusion?

- Select your answer -Cannot concludeConcludeItem 3 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.

- Select your answer -Men onlyWomen onlyBoth men and womenItem 10 prefer a slower pace of life. Women have a higher preference for a  - Select your answer -slowerfasterItem 11 pace of life, while men have a higher preference for a - Select your answer -slowerfasterItem 12 pace of life.

Answer 1

Solution:

Here, we have to use chi square test for independence of two categorical variables.

Null hypothesis: H₀: The preferred pace of life is independent of gender.

Alternative hypothesis: H_a: The preferred pace of life is not independent of gender.

We are given level of significance = α = 0.05

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

E = row total * column total / Grand total

We are given

Number of rows = r = 3

Number of columns = c = 2

Degrees of freedom = df = (r – 1)*(c – 1) = 2*1 = 2

α = 0.05

Critical value = 5.991465

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies (O)
	Gender
Preferred Pace of Life	Male	Female	Total
Slower	232	218	450
No Preference	19	25	44
Faster	89	47	136
Total	340	290	630

Expected Frequencies (E)
	Gender
Preferred Pace of Life	Male	Female	Total
Slower	242.8571	207.1429	450
No Preference	23.74603	20.25397	44
Faster	73.39683	62.60317	136
Total	340	290	630

(O - E)
-10.8571429	10.85714286
-4.74603175	4.746031746
15.6031746	-15.6031746

(O - E)^2/E
0.485378151	0.569064039
0.948571853	1.112118724
3.317024359	3.88892511

Chi square = ∑[(O – E)^2/E] = 10.32108

P-value = 0.005739

(By using Chi square table or excel)

P-value < α = 0.05

P-value is less than 0.01.

So, we reject the null hypothesis

There is sufficient evidence to conclude that the preferred pace of life is not independent of gender.

Part b

Required percentages for each gender are given as below:

Observed Frequencies (O)
	Gender
Preferred Pace of Life	Male	Female
Slower	68.2%	75.2%
No Preference	5.6%	8.6%
Faster	26.2%	16.2%
Total	100.0%	100.0%

From above table, it is observed that both men and women prefer a slower pace of life.