A researcher randomly interviews 800 customers about the waiting time for the next bus. The 95% confidence interval using an assumed population standard deviation for the population average waiting time is [1.5, 4.2] minutes. a. What is the sample average waiting time? b. What is the assumed population standard deviation? c. What is the 99% confidence interval using the assumed population standard deviation for the population waiting time? Is the interval larger than 95% confidence interval? d. If the researcher wants to take another sample and reduce the margin of error to 0.5 minutes at 95% confidence level, what is the minimum sample size? e. Suppose the researcher sampled another 25 customers and get the same sample average waiting time as in part (a). He realized that the assumed population standard deviation might be wrong, so decided to use the sample standard deviation 16. Assuming the population is normally distributed, construct a 90% confidence interval