Final answer:
To analyze the relationship between jogging and blood pressure, we perform a chi-square test for independence. The test involves comparing calculated chi-square statistic with a critical value, using given observed frequencies, expected frequencies, and an alpha level of 0.10 to either reject or accept the null hypothesis.
Step-by-step explanation:
Chi-Square Independence Test for Jogging and Blood Pressure
To determine if there is a relationship between jogging and blood pressure, we use a chi-square test for independence. The null hypothesis (H0) is that jogging and blood pressure are not related. The alternative hypothesis (H1) is that there is a relationship between jogging and blood pressure.
Calculation of Test Statistic
The test statistic for a chi-square test is calculated using the formula:
χ² = Σ((O - E)² / E)
Where O is the observed frequency and E is the expected frequency. To find the expected frequencies, we use the following formula for each cell of the table:
E = (row total * column total) / overall total
After calculating the expected frequencies and the chi-square statistic, we then compare the calculated chi-square statistic to the critical value from the chi-square distribution table based on the degrees of freedom (df) and the given alpha level (0.10). If the calculated chi-square statistic is greater than the critical value, we reject the null hypothesis, indicating a relationship between jogging and blood pressure.