Chapter 26, Problem 29E

a)

To determine

To find which test is appropriate.

Answer to Problem 29E

Chi-square test of Independence.

Explanation of Solution

Given:

  

When we want to check whether the two variables are independent. Therefore, here research wants to check whether the sex and party affiliation are independent. Hence, Chi-square test of Independence is appropriate.

b)

To determine

To state null and alternative hypotheses.

Answer to Problem 29E

  $H_0$ : Sex and party affiliation are independent.

  $H_a$ : Sex and party affiliation are not independent.

Explanation of Solution

Given:

  

The null and alternative hypotheses:

  $H_0$ : Sex and party affiliation are independent.

  $H_a$ : Sex and party affiliation are not independent.

c)

To determine

To check the conditions.

Answer to Problem 29E

All the conditions satisfied.

Explanation of Solution

Given:

  

There are three main conditions of Chi-square test:

Counts, Independent and expected counts are at least 5.

The data has given counts so the condition of counts satisfied.

Assuming that the respondents were randomly selected, so condition of independent is satisfied.

The smallest expected count is

  $\frac{40\times 97}{202}=19.2079$

Which is larger than 5 so all the conditions satisfied.

d)

To determine

To find P-value.

Answer to Problem 29E

P-value = 0.0884

Explanation of Solution

Using excel,

  

Therefore,

  ${\chi }^2$ = 4.85

P-value = 0.0884

e)

To determine

To state the conclusion.

Answer to Problem 29E

There is not sufficient evidence to support the claim that Sex and party affiliation are independent.

Explanation of Solution

Given:

  ${\chi }^2$ = 4.85

P-value = 0.0884

Decision: The p-value> 0.05, fail to reject H0.

Conclusion: There is not sufficient evidence to support the claim that Sex and party affiliation are independent.