Chapter 26, Problem 35E

a)

To determine

To find the expected count and explain why chi-square test is appropriate.

Answer to Problem 35E

The condition for chi-square test is satisfied.

Explanation of Solution

Given:

  

Formula:

  $E=\frac{Rowtotal\times Columntotal}{Total}$

  

The expected counts are greater than 5. Therefore, condition for chi-square test issatisfied. Hence, it is appropriate to use Chi-square test of Homogeneity.

b)

To determine

To find the degrees of freedom.

Answer to Problem 35E

The degrees of freedom are 3

Explanation of Solution

Given:

  

Formula:

  $df=(r-1)(c-1)$

The number of rows = r = 4

The number of columns = c = 2

Therefore, the degrees of freedom are:

  $df=(4-1)\times (2-1)=3$

One row decreases from table as compare to example 33 so number of degrees of freedom is decreased by 1.

c)

To determine

To perform chi-square test.

Answer to Problem 35E

There is sufficient evidence to reject the claim that grade distribution is the same for all teachers.

Explanation of Solution

Given:

  

The null and alternative hypotheses:

  $H_0$ : The grade distribution is the same for all teachers.

  $H_a$ : The grade distribution is different among teachers.

Using excel,

  

  ${\chi }^2$ = 9.31 and P-value = 0.0255

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

Conclusion: There is sufficient evidence to reject the claim that grade distribution is the same for all teachers.