Question

Q3. Hypothesis Testing with a Z Test (12 points)

According to the CDC report, the mean life expectancy in the US population is currently (µ) 78.6 years with a standard deviation (σ) of 12. A researcher examined the age of death of 400 people recently recorded in several Arizona hospitals and calculated the mean to be 79.5 years old. He runs a two-tailed Z test with α = .05 to see if Arizona has a significantly different life expectancy compared to the US population. Because the researcher is not predicting a direction, the hypotheses should be non-directional and the test should be two-tailed.

e. Calculate the standardized effect size. (1 point: .5 if the process is correct but the result was calculated incorrectly)

f. Write 1-2 sentences to answer the research question (you can use the wording from the hypotheses or explain it in another way) (1 point)

Answer the following questions based on this alternative scenario:

Because a sample of 400 people is small, it may not represent the state of Arizona adequately. So the researcher continues to collect data until the sample becomes 900. The average life expectancy remains 79.5, the same as the previous scenario.

g. What is the standard error now? (.5 point) How is it different from the hypothesis test with the smaller sample in question (a)? (.5 point)

h. What is the Z statistic now? (.5 point) How is it different from the hypothesis test with the smaller sample in question (b)? (.5 point)

i. What is the conclusion of the hypothesis test now? (.5 point) How is it different from the hypothesis test result with the smaller sample in question (d)? (.5 point)

j. What is the standardized effect size now? (.5 point) How is it different from the effect size with the smaller sample in question (e) above? (.5 point)

k. Based on the answers to questions g-j, discuss the effects of simply increasing the sample size while everything else remains the same. (1 point) Provide one reason why it is a good idea to have a larger sample for a study. (1 point)

Answer 1

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