91Ó°ÊÓ

Check whether or not the data provide sufficient evidence to conclude that an association exists between religiosity and education.

Step 1:

The test hypotheses are given below:

Null hypothesis:

H0 : There is no association exists between religiosity and education.

Alternative hypothesis:

H1 : There is an association exists between religiosity and education.

Step 2: Decide the level of significance.

Here, the level of significance is, 5%.

Step 3:

Find the expected frequency and test statistic.

MINITAB procedure:

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

Step 2: In Columns containing the table, enter the column of Basic, Secondary and Advanced.

Step 3: In Rows, select RELIGIOUSITY.

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

Step 5: Click OK.

Pearson Chi-square $=13.322,\mathrm{DF}=6$, p-Value =0.038

Likelihood Ratio Chi-Square=12.814, DE=6,P-Value=0.046

From the MINITAB output, the value of the chi-square statistic is 13.322

Step 4:

Find the P-value.

From the MINITAB output, the P-value is 0.038

Step 5:

Rejection rule:

If P-value $≤\mathrm{Î\pm }$, then reject the null hypothesis.

Here, the P-value is lesser than the level of significance.

That is, P-value (=0.038)<(=0.05) .

Therefore, the null hypothesis is rejected at 5% level.

Thus, the results are statistically significant at 5% level of significance.

Thus, the data provide sufficient evidence to conclude that an association exists between religiosity and education at the 5% significance level.

Decide the significance level.

Here, the level of significance is $\mathrm{Î\pm }=0.01$.

p-value approach:

From part (a)., the value of the chi-square statistic is $13.322$and the P-value is $0.038$.

Here, the P-value is greater than the level of significance.

That is, P-value $(=0.038)>\mathrm{Î\pm }(=0.01)$.

Therefore, the null hypothesis is not rejected at 1% level.

Thus, the results are not statistically significant at 1% level of significance.