. We surveyed a sample of people (N=200) about their age and their position on raising the retirement. Below is a bivariate table showing age (young and old) by position on raising the retirement age (yes or no).

Table 1. Age and Opinion About Retirement Age

Young

Old

Total

Yes

33.33%

62.50%

45.00%

(40)

(50)

(90)

No

66.67%

37.50%

55.00%

(80)

(30)

(110)

Total

100.0%

100.0%

100.0%

(120)

(80)

(200)

A. Is there an effect of age on positions on raising the retirement age in our sample? If so, what is the size and magnitude (weak, moderate, strong) of that relationship?

There is an moderate relationship.

We want to know whether the difference observed in our sample is likely to be present in the population. We need to perform a chi-square test. We'll set an alpha level of 0.10

B. State your hypotheses:

H₁:

H₀:

What is your independent variable?

What is your dependent variable?

C. Find the expected frequencies for each of the cells.

Table 2. Expected Frequencies

Young

Old

Total

Yes

45.00%

45.00%

45.00%

(90)

No.

55.00%

55.00%

55.00%

(110)

Total

100.0%

100.0%

100.0%

(120)

(80)

(200)

D. Calculate the chi-square test statistic.

Status X Opinion

Young/Yes

Young/No

Old/Yes

Old/No

E. Calculate the degrees of freedom.

=

F. Using the chi-square table, find the critical value the degrees of freedom and alpha level.

CV =

G. Evaluate your hypothesis.

Is your chi-square test statistic greater than your critical value?

Do we reject or fail to reject the null hypothesis?

Interpret your conclusion.

2. The bivariate table below shows the results of a survey in which men and women were asked whether they favor legalizing marijuana.

Sex

Should marijuana be legal?

Male

Female

Total

Yes

61.0% (430)

50.9% (440)

55.4%(870)

No

39.0% (275)

49.1% (425)

44.6%(700)

Total

100.0% (705)

100.0% (865)

100.0% (1570)

A. Is there an effect of gender on support for legalizing marijuana in our sample? If so, what is the size and magnitude (weak, moderate, strong) of that relationship?

We want to know whether the difference observed in our sample is likely to be present in the population. We need to perform a chi-square test. We'll set an alpha level of 0.01

B. State your hypotheses:

H₁:

H₀:

What is your independent variable?

What is your dependent variable?

C. Find the expected frequencies for each of the cells.

Table 2. Expected Frequencies

Male

Female

Total

Yes

55.40%

55.40%

55.40%

(870)

No.

44.60%

44.60%

44.60%

(700)

Total

100.0%

100.0%

100.0%

(705)

(865)

(1570)

D. Calculate the chi-square test statistic.

Status X Opinion

Male/Yes

Male/No

Female/Yes

Female/No

E. Calculate the degrees of freedom.

=

F. Using the chi-square table, find the critical value the degrees of freedom and alpha level.

CV =

G. Evaluate your hypothesis.

Is your chi-square test statistic greater than your critical value?

Do we reject or fail to reject the null hypothesis?

Interpret your conclusion.