Question

Each year, the Chapman University Survey of American Fears asks a random sample of Americans whether they are afraid of various issues. One question on the survey asks about air pollution. The table below reports the number of individuals surveyed in 2018 who responded that they were either afraid or not afraid of air pollution, by political affiliation.

	Republican	Independent	Democrat	Total
Not afraid of air pollution	61	94	28	183
Afraid of air pollution	263	367	376	1,006
Total	324	461	404	1,189

We’d like to know if, in the American population in 2018, fear of air pollution depends on a person’s political affiliation.

1) Set-up the corresponding null and alternative hypotheses. The appropriate alternativehypothesis is

Group of answer choices

H_a: Republicans are more likely than Democrats to fear air pollution in the US

H_a: There is some association between political affiliation and fear of air pollution in this population

Ha: Republicans and Democrats are not equally likely to fear air pollution in the US

H_a: Democrats are more likely than Republicans to fear air pollution in the US

Ha: Republicans and Democrats are equally likely to fear air pollution in the US

H_a: There is no association between political affiliation and fear of air pollution in this population

2) Which inference procedure should be used?

A - two sample t procedure for two means

B - ANOVA for several means

C - chi-square for two-way tables

D - z procedure for a proportion

E - one sample or matched-pairs t procedure for a mean

F - chi-square for goodness of fit

3) The value of the corresponding test statistic is:

4) What are the conditions for this inference procedure?

A - Normal data AND large enough expected counts.

B - Random selection without repeated measures AND large enough expected counts.

C - Independent random samples AND normal data AND large enough total sample size.

D - Independent random samples AND normal data or large enough total sample size.

E - Independent random samples AND normal data or large enough total sample size AND similar sample standard deviations.

F - One random sample AND normal data AND large enough sample size.

G - One random sample AND normal data or large enough sample size.

H - One random sample AND large enough counts of successes and failures in the sample.

I - Independent random samples AND normal data AND large enough total sample size AND similar sample standard deviations.

J - One random sample AND large enough expected counts.

5) Assuming for now that the conditions for inference are met, conclude in context based on this hypothesis test.

(Be sure to be very specific and to site your computed P-value).

Answer 1

1. Ha: There is some association between political affiliation and fear of air pollution in this population

because we want to check dependency of fear on political affiliation as a whole.

2. C - chi-square for two-way tables

because we will be comparing all the attributes for their independence.

3.

4. The conditions for this inference are :

For chi square test of independence of attributes, the conditions are completely different.

1. The categories should be independent
2. The frequencies or cell should represent count.
3. There should be atleast 5% or more in each cell.
4. Large sample size

5. Conclusion is shown in 3rd part.

Please rate my answer and comment for doubt.