Question

Fran is training for a marathon and she wonders if she will receive better training is she runs with a group rather than on her own . She wants to know if there is a significant difference in the number of miles run each week between group runners and individual runners . The interviews 32 people that she knows train in groups , and finds that they average 49 miles per week with a standard deviation of 4.2 miles . The also interviews 30 people who she knows that train on their own and finds that they runon average 47.2 miles per week with a standard deviation of 4.8 miles . Test Fran's claim at .05

Answer 1

To determine if there is a significant difference in the number of miles run each week between group runners and individual runners, a hypothesis test can be conducted. The null hypothesis states that there is no significant difference, while the alternative hypothesis suggests that there is. A two-sample t-test can be used to compare the mean number of miles run per week for each group.

Step-by-step explanation:

In order to determine if there is a significant difference in the number of miles run each week between group runners and individual runners, we can conduct a hypothesis test. Let's define the null and alternative hypotheses:

Null hypothesis (H0): There is no significant difference in the number of miles run each week between group runners and individual runners.

Alternative hypothesis (Ha): There is a significant difference in the number of miles run each week between group runners and individual runners.

To test Fran's claim at a significance level of 0.05, we need to perform a two-sample t-test. We'll compare the mean number of miles run per week for the group runners and the individual runners. We have the sample means, sample standard deviations, and sample sizes for both groups. Using the t-test, we can calculate the test statistic and compare it to the critical value to determine if there is a significant difference.