12.81 Learning at Home. M. Stuart et al. studied various aspects of grade-school children

and their mothers and reported their findings in the article "Learning to Read at Home

and at School" (British Journal of Educational Psychology, 68(1), pp. 3-14).

The researchers gave a questionnaire to parents of 66 children in kindergarten

through second grade. Two social-class groups, middle and working, were identified based on the mother's occupation.

a. One of the questions dealt with the children's knowledge of nurs-

Check whether or not the Assumption 1 and 2 satisfied for chi-square independence test.

Find the expected frequency by using MINITAB.

MINITAB procedure:

Step 1: Choose Stat > Tables > Chi-Square test for association.

Step 2: In Columns containing the table, enter the column of A few, Some, and Lots.

Step 3: In Rows, select SOCIAL CLASS.

Step 4: Under Statistics, select Chi-square test, Display counts in each cell, Display marginal counts and expected cell counts.

Step 5: Click OK.

The general assumption is given below.

Assumption:

- All expected frequencies are at least 5

- At most $20\%$of the expected frequencies are less than 5

- The selected sample should be a simple random sample

From the MINITAB output, it is clear that all expected frequencies are at least 1 . But 2 out of 6 expected frequencies are less than 5 . Hence, the Assumption 1 is satisfied and the Assumption 2 is not satisfied. Thus, the chi-square independence test is not used in the given data.

Check whether or not the Assumption 1 and 2 satisfied for chi-square independence test.

Find the expected frequency by using MINITAB.

MINITAB procedure:

Step 1: Choose Stat $>$ Tables $>$ Chi-Square test for association.

Step 2: In Columns containing the table, enter the column of Never, Sometimes, and Often.

Step 3: In Rows, select SOCIAL CLASS

Step 4: Under Statistics, select Chi-square test, Display counts in each cell, Display marginal counts and expected cell counts.

Step 5: Click OK.

Now,

Minitab output

The general assumption is given below:

Assumption:

- All expected frequencies are at least $1 .$

- At most $20 \%$ of the expected frequencies are less than $5 .$

- The selected sample should be a simple random sample

From the MINITAB output, it is clear that all expected frequencies are at least 1 and all expected frequencies are greater than 5. Hence, the Assumption 1 and 2 is satisfied. Thus, the chi-square independence test is used in the given data.

Check whether or not there is association exists between frequency of games and social class.

Step 1

The test hypotheses are given below:

Null hypothesis:

H0 : The data do not provide sufficient evidence to conclude that the parents played

"I Spy" games with their children.

Alternative hypothesis:

H1: The data provide sufficient evidence to conclude that the parents played "I Spy" games with their children.

Step 2: Decide the level of significance.

Here, the level of significance is, 1%

Step 3:

Find the test statistic and p-value.

From the MINITAB output, the value of the chi-square statistic is 8.715.

Step 4

Find the P-value.

From the MINITAB output, the P-value is 0.013.

Step 6. Interpretation

Thus, the data provide sufficient evidence to conclude that the parents played "I Spy" games with their children at the 1 % significance level.