### Explain when a z-test would be appropriate over a t-test

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Question -1:

Explain when a z-test would be appropriate over a t-test 1. There is a new drug that is used to treat leukemia. The following data represents the remission time in weeks for a random sample of 21 patients using the drug.

 10 7 32 23 22 6 16 11 20 19 6 17 35 6 10 34 32 25 13 9 6

Let X be a random variable representing the remission time in weeks for all patients using the new drug. Assume that the distribution of x is normal. A previously used drug treatment has a mean remission time of 12.5 weeks. Does the data indicate that the mean remission time using the new drug is different from 12.5 week at a level of significance of 0.01?

State the Null Hypothesis

State the Alternatice Hypothesis

State the Level of significance

State the Test Statistic

Question-2:

Researchers routinely choose an alpha level of 0.05 for testing their hypotheses. What are some experiments for which you might want a lower alpha level (e.g., 0.01)? What are some situations in which you might accept a higher level (e.g., 0.1)?2. We wish to test the claim that the mean body mass index (BMI) of men is equal to the mean BMI of women. Use the data to the right to test this claim.

 Men Women 20 29 37 28 46 20 23 28 20 42 23 45 21 19 15 45 20 16 28 32 27 38 20 45 30 41 22 34 27 28 38 21 29 42 20 21 16 30 27 28 42 30 37 43 39 40 39 16 32 44 16 15 21 16 26 20 17 41 39 16

State the Null Hypothesis

State the Alternatice Hypothesis

State the Level of significance

State the Test Statistic

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