Question

two friends, karen and jodi, work different shifts for the same ambulance service. they wonder if the different shifts average different numbers of calls. looking at past records, karen determines from a random sample of 34 shifts that she had a mean of 5.3 calls per shift. she knows that the population standard deviation for her shift is 1.4 calls. jodi calculates from a random sample of 41 shifts that her mean was 4.7 calls per shift. she knows that the population standard deviation for her shift is 1.1 calls. test the claim that there is a difference between the mean numbers of calls for the two shifts at the 0.02 level of significance. let karens shifts be population 1 and let jodis shifts 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 sufficient evidence at a 0.02 level of significance to support karens and jodis claim that there is a difference between the mean numbers of calls for their shifts. we reject the null hypothesis and conclude that there is sufficient evidence at a 0.02 level of significance to support karens and jodis claim that there is a difference between the mean numbers of calls for their shifts. we fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.02 level of significance to support karens and jodis claim that there is a difference between the mean numbers of calls for their shifts. we reject the null hypothesis and conclude that there is insufficient evidence at a 0.02 level of significance to support karens and jodis claim that there is a difference between the mean numbers of calls for their shifts.

Explanation:

Step1: Understand hypothesis - testing conclusion

In hypothesis - testing, if we fail to reject the null hypothesis, it means there is insufficient evidence to support the alternative hypothesis. If we reject the null hypothesis, there is sufficient evidence to support the alternative hypothesis. Here, the null hypothesis $H_0:\mu_1=\mu_2$ (no difference in means) and the alternative hypothesis $H_1:\mu_1
eq\mu_2$ (difference in means).

Step2: Analyze the claim

Karen and Jodi claim that there is a difference between the mean numbers of calls for their shifts. To support this claim, we need to reject the null hypothesis.

Step3: Interpret the decision

If we fail to reject the null hypothesis, we conclude that there is insufficient evidence at the 0.02 level of significance to support their claim. If we reject the null hypothesis, we conclude that there is sufficient evidence at the 0.02 level of significance to support their claim.

Answer:

We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.02 level of significance to support Karen's and Jodi's claim that there is a difference between the mean numbers of calls for their shifts.