Patients with rheumatoid arthritis are at a greater risk of developing osteoporosis. The reasons are not well understood due to the difficulty in qualitatively assessing bone metabolism and mineral content. A researcher measures human calcitonin (HCT) levels in men with rheumatoid arthritis. The researcher randomly selects 43 men with rheumatoid arthritis and measured the mean HCT level of 33.8 pg/mL. Assume that HCT for individuals with rheumatoid arthritis follows a normal distribution with standard deviation = 23.6 pg/mL.

1. For a 95% level of confidence what is the appropriate critical value Z*that needs to be used to calculate the margin of error? Determine the value of the critical value using a table or preferred technological tool.

2. Determine the margin of error for HCT levels.

3. Create a 95% confidence interval for the population mean HCT.

4. Explain in detail what the 95% Confidence Interval for the mean HCT represents within this context.

5. What is the effect on the interval width if we decreased or increase the confidence level to 90% or 99% respectively? (Hint, create the intervals)

6. Describe the effect on your confidence interval if you increase or decrease the sample size.

7. Describe a situation where a researcher would want to use a larger confidence level than 95% and a situation where a smaller confidence level would be preferred.

8. Create a short summary explaining the process of inference (making an assertion about the population using sample data). Include how its performed, necessary conditions, sample size requirement, and its connection to the sampling distribution.