Hypothesis Testing with a Z Test According to the CDC report, the mean life expectancy in the US population is currently (µ) 77.8 years with a standard deviation (σ) of 14. A researcher examined the age of death of 55 people recently recorded in several Arizona hospitals and calculated the mean to be 80.6 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. Answer the following questions based on this alternative scenario: Because a sample of 55 people is small, it may not represent the state of Arizona adequately. So, the researcher decides to continue to collect data until the sample becomes 115. The average life expectancy remains 80.6, the same as the previous scenario. All other aspects of the study remain unchanged. i. What is the standard error with this sample? What is the Z statistic with this sample? j. Compare the Z statistic with the appropriate critical Z value and then draw a conclusion about the result of the hypothesis test. What is the answer to the research question now? - Do you “reject” or “fail to reject” the null hypothesis? - What is the answer to the research question? k. Calculate the standardized effect size.
Hypothesis Testing with a Z Test
According to the CDC report, the mean life expectancy in the US population is currently (µ) 77.8 years with a standard deviation (σ) of 14. A researcher examined the age of death of 55 people recently recorded in several Arizona hospitals and calculated the mean to be 80.6 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.
Answer the following questions based on this alternative scenario:
Because a sample of 55 people is small, it may not represent the state of Arizona adequately. So, the researcher decides to continue to collect data until the sample becomes 115. The average life expectancy remains 80.6, the same as the previous scenario. All other aspects of the study remain unchanged.
i. What is the standard error with this sample? What is the Z statistic with this sample?
j. Compare the Z statistic with the appropriate critical Z value and then draw a conclusion about the result of the hypothesis test. What is the answer to the research question now?
- Do you “reject” or “fail to reject” the null hypothesis?
- What is the answer to the research question?
k. Calculate the standardized effect size.
l. Based on the hypothesis test results with the two samples (one with 55 subjects and the other with 115 subjects), how did the increase in sample size impact the test results in terms of the Z statistic and the effect size?
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