Question

A medical researcher wonders if there is a relationship between exercise level and smoking. The researcher collects the following data from a survey of 171 randomly selected college students in California. In this results table, the observed count appears above the expected count in each cell. Total Heavy Regularly Occasionally Never Smoker Smoke Smoke Smoke Observed 17 12 87 Expected 21.1 11.2 14.0 Frequently Exercise 78.7 125 25 Observed Sometimes Expected Exercise 13 8.9 8 6.0 4.8 33.3 53 20 Total Observed 30 16 112 178 The medical researcher conducts a chi-square test of homogeneity to determine if there are statistically significant differences in the distribution of responses for frequently exercise and sometimes exercise. The chi-square test statistic for this data is 8.1077 with a P-value of 0.04384. What can the medical researcher conclude?

Answer 1

Solution:

Given:

Total Heavy Regularly Occasionally Never Smoker Smoke Smoke Smoke Observed 17 9 87 Frequently Expected 21.1 11.2 14.0 78.7 Exercise 12 125 Observed 13 8 Sometimes Expected 25 33.3 4.8 6.0 Exercise 53 Total Observed 30 16 2 0 112 178

We have to test if there are statistically significant differences in the distribution of responses for frequently excercise and sometimes excercise.

Thus hypothesis are:
H0: there are NO statistically significant differences in the distribution of responses for frequently excercise and sometimes excercise.

Vs

Ha: there are statistically significant differences in the distribution of responses for frequently excercise and sometimes excercise.

Chi-square test statistic =8.1077 and P-value = 0.04384

Decision rule: Reject null hypothesis H0 , if P-value < 0.05 level of significance otherwise we fail to reject H0.

Since P-value = 0.04384 < 0.05 level of significance , we reject null hypothesis H0.

Thus conclusion is:

There are statistically significant differences in the distribution of responses for frequently excercise and sometimes excercise.