4. A study aims to compare the body mass index (BMI, kg/m2) of women aged 45 years residing within and outside the capital area. The mean and standard deviation for each group of individuals is presented in Table 8.7.

Please answer the following questions:

(a) Which tests could be employed for testing the population mean differences in BMI? Please give your reasons.

(b) hat do you think about the relationship between the t-test and Z-test ? Under what conditions could the Z-test be used as a substitute for the t-test, and which theorem is needed to guarantee such a substitution?

(c) Please conduct the hypothesis tests and interpret the results with a summary report.