Refer to the dataset "glycemic_control.xlsx".This dataset presents data from a randomized trial with 64 young adult participants with type I diabetes, free of any major comorbidities. Patients were randomized to either intensive insulin therapy (IIT) or the standard of care available without IIT. The data present measurements at the final time-point of the study. The primary quantity of scientific interest in this study was the participants' hemoglobin A1c percentage (HbA1c %), a measure of how well a patient has controlled their blood glucose level. High values of HbA1c % indicate poor control, while values of HbA1c % closer to zero indicate better glycemic control. Each row in the dataset corresponds to one participant in the study.

Variables in this data include:

IDnum: Participant ID (1 to 64)

gender: Participant gender (1 for male, 2 for female)

age: Participant age (years)

insulin: Indicator of whether participant was randomized to IIT (insulin=1) or standard of care (insulin=0)

hba1c: Hemoglobin A1c percentage for participant

Question modeled from: The DCCT Research Group, "Diabetes Control and Complications Trial (DCCT): Results of Feasibility Study." - Diabetes Care(1987)

1a.

Investigators are interested in comparing average HbA1c % between those randomized to IIT and those randomized to standard of care. Specifically, they wish to assess whether there is evidence that the average HbA1c % may be different in the two populations.

Propose a statistical hypothesis test that can be used to answer the investigators' research question.

State the null and alternative hypotheses in words (that apply to this problem) and symbols.

State the assumptions for this hypothesis test.

Are the assumptions met? Explain briefly. (In particular, do the HbA1c values need to be normally distributed?

If so, are they normally distributed in this problem? Explain very briefly and show graphically.)

1b.

Regardless of your answer to question 1a, conduct the hypothesis test.

For each treatment group, state the average and standard deviation for HbA1c % values .

Calculate the test statistic for your hypothesis test.

Calculate the p-value and state the degrees of freedom if appropriate.

Interpret the p-value for a non-statistician in the context of the problem. [The p-value is a probability .... What is it the probability of in THIS problem? Do NOT use the words "null hypothesis."] Do NOT simply state whether or not the result is statistically significant.

If you use software, state the command you used and include a portion of the output. If you used a table, state that.

1c.

Find a 90% confidence interval for the average difference in HbA1c % values between treatment groups.

Interpret this confidence interval in language suitable for a non-statistician.

Which treatment option would you recommend to a patient with type I diabetes who wishes to improve their glycemic control?

Briefly explain. If you use software, state the command you used and include a portion of the output. If you calculate the 90% confidence interval by hand then show all your work.