Several drugs are used to treat diabetes. A sales specialist for a leading pharmaceutical company randomly sampled the records of 10 sales districts to estimate the number of new prescriptions that had been written during a particular month for her company's new diabetes drug. The numbers of new prescriptions were as follows:
210, 240, 190, 275, 290, 265, 312, 284, 261, 243
a. Find a 90% confidence interval for the average number of new prescriptions written for this new drug among all the sales districts.
b. Assuming that the confidence level remains constant, what sample size is needed to reduce by half the margin of error of the confidence interval in part (a)?
Need answer in the following format:
1. The problem statement.
2. Your approach.
3. Assumptions.
4. The confidence level.
5. The result and its interpretation.