Question

There are a number of studies which show that women engage in more private religious rituals and daily prayer than men, who tend to engage in more public religious rituals. A researcher would like to discover if there is a relationship between gender and religious type, that is extrinsically religious (publicly religious), intrinsically religious (personally religious) or nonreligious. Perform the appropriate test (α = 0.05)

Male extrinsic 9

Female extrinsic 9

Male intrinsic 14

Female intrinsic 16

Male non religious 12

Female non religious 6

Answer 1

The given problem has to be solved using the Chi-square test of association. In order to do so, define the null and alternate hypothesis as shown below:

: The gender and religious type are independent, that is, gender does not influence the religious beliefs of a person, versus,

: The gender and religious type are dependent, that is, gender influences the religious beliefs of a person.

The observed frequencies, , can be tabulated in the following format:

Religious Type\ Gender	Extrinsic	Intrinsic	Non-religious	Total
Male	9	14	12	35
Female	6	16	6	28
Total	15	30	18	63

Now, the expected frequencies need to computed using the formula:

where column total and row total is sum of the values contained in the column and row, respectively, of the cell whose expected counted need to be computed.

The table showing the expected frequencies, , is shown below:

Thus, the following table is obtained for :

The test statistic value, , is calculated using the following formula:

The test statistic value follows the chi square distribution, with degrees of freedom, where, m and n denotes the number of rows and columns respectively.

The table contains two rows and three columns. Hence, . This implies:

Therefore, the right tail critical value at   level of significance is and 2 degrees of freedom is compued using the formula in MS-Excel. The screenshot is shown below:

Hence, .

Since, the calculated value of test statistic is less than the critical value, so, there is an insufficient evidence to reject the null hypothesis and it can be concluded that the gender and religious type are not associated with each other.