Question

question 1 of 6, step 3 of 3
2/20
correct
fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. she interviews 34 randomly selected people who train in groups, and finds that they run a mean of 41.4 miles per week. assume that the population standard deviation for group runners is known to be 2.6 miles per week. she also interviews a random sample of 42 people who train on their own and finds that they run a mean of 42.4 miles per week. assume that the population standard deviation for people who run by themselves is 1.4 miles per week. test the claim at the 0.10 level of significance. let group runners training for marathons be population 1 and let individual runners training for marathons be population 2.
step 3 of 3: draw a conclusion and interpret the decision.
answer
we fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.10 level of significance to support frans claim that there is a significant difference between the mean number of miles run each week by group runners and individual runners.
we reject the null hypothesis and conclude that there is insufficient evidence at a 0.10 level of significance to support frans claim that there is a significant difference between the mean number of miles run each week by group runners and individual runners.
we fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.10 level of significance to support frans claim that there is a significant difference between the mean number of miles run each week by group runners and individual runners.
we reject the null hypothesis and conclude that there is sufficient evidence at a 0.10 level of significance to support frans claim that there is a significant difference between the mean number of miles run each week by group runners and individual runners.

Explanation:

Step1: Recall hypothesis - testing decision - rule

If the p - value is greater than the significance level ($\alpha$), we fail to reject the null hypothesis. If the p - value is less than or equal to $\alpha$, we reject the null hypothesis. Here, $\alpha = 0.10$.

Step2: Interpret the conclusion

When we fail to reject the null hypothesis, it means that there is not enough evidence to support the claim. When we reject the null hypothesis, it means that there is enough evidence to support the claim.

Answer:

We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.10 level of significance to support Fran's claim that there is a significant difference between the mean number of miles run each week by group runners and individual runners.