Chapter 26, Problem 28E

a)

To determine

To find which test is appropriate.

Answer to Problem 28E

Chi-square test of Homogeneity.

Explanation of Solution

Given:

  

When we want to check whether the distribution of one variable is the same in multiple group then we use Chi-square test of Homogeneity. Therefore, here research wants to check the origin of the cars driven by students and staff is the same for both groups. Hence, Chi-square test of Homogeneity is appropriate.

b)

To determine

To state null and alternative hypotheses.

Answer to Problem 28E

  $H_0$ : The origin of the cars driven by students and staff is the same for both groups.

  $H_a$ : The origin of the cars driven by students and staff is different among the groups.

Explanation of Solution

Given:

  

The null and alternative hypotheses:

  $H_0$ : The origin of the cars driven by students and staff is the same for both groups.

  $H_a$ : The origin of the cars driven by students and staff is different among the groups.

c)

To determine

To check the conditions.

Answer to Problem 28E

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.

The data is originated from a random survey, so condition of independent is satisfied.

The smallest expected count is

  $\frac{45\times 164}{359}=20.5571$

Which is larger than 5 so all the conditions satisfied.

d)

To determine

To find P-value.

Answer to Problem 28E

P-value = 0.0200

Explanation of Solution

Using excel,

  

Therefore,

  ${\chi }^2$ = 7.83

P-value = 0.0200

e)

To determine

To state the conclusion.

Answer to Problem 28E

There is sufficient evidence to reject the claim of same proportions in all the groups.

Explanation of Solution

Given:

  ${\chi }^2$ = 7.83

P-value = 0.0200

Decision: The p-value< 0.05, reject H0.

Conclusion: There is sufficient evidence to reject the claim of same proportions in all the groups.