Instructions:
- Use this Word document to record the calculation/analysis process and the answers.
- All answers must be in this Word document
- Follow the instructions for each specific question as each will have different requirements.
- Upload the document when you are finished. (Double-check that the document has loaded successfully and that you uploaded the correct/completed document, not the blank version!)
Q1. Use the estimation method to calculate and interpret a confidence interval. (7 pts.)
Suppose we are sampling from a population that is known to be normal with a standard deviation of σ = 5. However, the mean is unknown, so we will need to estimate it using our sample mean.
A. For a sample mean (Xbar) = 20 and a sample size N = 25, compute a 95% confidence interval for (Show the process you used to determine the CI bounds.)
B. In your own words, explain the meaning of the confidence interval you have found.
Q2. Use the estimation method and compare models to test a hypothesis. (9 pts.)
You are part of a trivia team and have tracked your team’s performance since you started playing, so you know that your scores are normally distributed with μ = 78 and σ = 12. Recently, a new person joined the team, and you think the scores have gotten better. Your goal is to answer the question: Are the new scores on average significantly better than 78? Follow the instructions below to determine the answer.
A. Calculate the sample mean of the following 9 weeks’ worth of score data: 94, 77, 74, 75, 91, 97, 93, 87, 86.
B. Compute a 95% confidence interval for (Show the process you used to determine the CI bounds.)
C. From the confidence interval you obtained, can we conclude that the team scores are significantly better since the new person joined the team? Explain your answer.
Q3. Manually perform a z-test. (9 pts.)
According to the CDC report, the mean life expectancy in the US population is currently (µ) 82.6 years with a standard deviation (σ) of 10. A researcher examined the age of death of 250 people recently recorded in several Arizona hospitals and calculated the mean to be 76.5 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. For this question, leave answers in their original decimal places.
A. What are the null hypothesis and alternative hypothesis? Write each one in words and with symbols.
H0:
Null Hypothesis:
H1:
H1: Alternative/Research Hypothesis:
B. Calculate the standard error. (Show your calculation process.)
σ M =
C. Calculate the Z statistic. (Show your calculation process.)
z =
D. Determine the critical z value(s). Explain how to find the answer.
E. What is the conclusion of the hypothesis test (do you “reject” or “fail to reject” the null hypothesis)? What is the rationale?
F. Answer the research question (you can use the wording from the hypotheses or explain it in another way).
G. Calculate the standardized effect size. No need to round. (Show your calculation process.)
Cohen’s d = (M-μ)/ σ =
