Research Scenario

Measures of height from the general population of adult males in the United States form a normal distribution with am = 69 ands = 4 (inches). Epidemiological studies have shown that growth hormone deficiency in childhood increases the risk for short stature in adulthood. Using data from a cohort study, a researcher obtained a sample of n = 144 adult males with growth hormone deficiency whose average height wasx= 68. Do these data indicate that growth hormone deficiency is associated with short stature in this sample? Test withalpha=.05.

Note

= population mean

x = sample mean

s = standard deviation

Step 1: Set up your hypothesis and determine the level of significance

State the null hypothesis

1. In written format

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1. In mathematical format

Answer:

State the alternative hypothesis

1. In written format

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1. In mathematical format

Answer:

Determine the Level of significance

1. Based on information in the scenario, what is the level of significance to be used?

Answer:

Step 2: Select the appropriate test statistic

1. The appropriate test statistic for the above scenario is the one-sample z test. What is a Z test? Describe why this is the appropriate test for the scenario?

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Step 3: Set up the decision rule

1. Based on thelevel of significance you set in Step 1 (Question 5) and whether your alternative hypothesis is directional or non-directional, what is your decision rule? (In other words, what is your rejection region?)

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Step 4: Compute the test statistic

1. Calculate the z statistic. Please show your work.

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Step 5: Conclusion

1. Do you reject or fail to reject the null hypothesis?

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1. Is height affected by growth hormone deficiency in this sample?

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