Question

A 2017 Raihan et al. study of 10,478 Bangladesh children tracked the washing habits of the childrens' mothers via survey to understand the relationship of these habits with childhood wasting. The data provided include responses from mothers to two items on this survey. The first variable represents a household's access to food:
food secure, mildly food insecure, moderately food insecure, or severely food insecure. The second variable represents the mothers' responses when asked whether they wash their hands with soap before preparing food.
Suppose the researchers wish to study a potential relationship between washing habits and food security. Use software to conduct a chi-square test for independence at a significance level of a = 0.05 to determine if there is a relationship between washing habits and food security. You may find these software manuals helpful.
Determine the chi-square test statistic for the chi-square test for independence based on this data. Please round your answer to the nearest three decimal places.
chi-square statistic = 207.279 Incorrect
Based on the chi-square statistic and its corresponding P-value select the statement that represents the correct conclusion for the chi-square test for independence.
a. Because the chi-square statistic is very large and the P-value is less than the significance level, there is sufficient evidence of a relationship between food security and whether mothers in Bangladesh households wash their hands with soap before preparing food.
b. Because the chi-square statistic is very large and the P-value is greater than the significance level, there is sufficient evidence of a relationship between food security and whether mothers in Bangladesh households wash their hands with soap before preparing food.
c. Because the chi-square statistic is very large and the P-value is less than the significance level, there is insufficient evidence of a relationship between food security and whether mothers in Bangladesh households wash their hands with soap before preparing food.
d. Because the chi-square statistic is very large and the P-value is greater than the significance level, there is insufficient evidence of a relationship between food security and whether mothers in Bangladesh households wash their hands with soap before preparing food.

Answer 1

According to the test statistic given by the chi-square distribution, it is found that the correct option is:

d. Because the chi-square statistic is very large and the P-value is greater than the significance level, there is insufficient evidence of a relationship between food security and whether mothers in Bangladesh households wash their hands with soap before preparing food.

At the null hypothesis, we test if there is no relationship between washing habits and food security.

At the alternative hypothesis, we test if there is a relationship between washing habits and food security.

The test statistic is $\chi^2 = 207.279$.

• Now, using a chi-square distribution calculator, we have to find the p-value associated with this test statistic.
• Using the calculator, with 10478 - 1 = 10,477 df, the p-value is of 1, which is higher than the significance level, hence there is no relationship, and option d is correct.

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