Some latest study shows that college students are increasingly skimping on their sleep. A researcher from a small community college wants to estimate the mean weekdays sleep time of its students. He takes a random sample of 77 students and records their weekday mean sleep time as 6.70 hours. Assume that the population standard deviation is fairly stable at 1.50 hours.(a) Construct a 95% confidence interval for the population mean weekday sleep time of all students of this college.Use the following table of z?2 for most common ? values.Find z?2= Round the margin of error and confidence interval values to 2 decimal places.Calculate the margin of error E=What is the 95% confidence interval????(b) If the researcher wants to be 99% confident that the sample mean is within 0.30 hours (or 18 min) of the true population mean weekday sleep time, how many students should he include in the sample?Find z?2= Round your answer (n) UP to the next whole number.The required sample size n is

(b) Find the critical value (s). In the first box please indicate the sign(s), and in the second box enter the numeric value. Use the following table of z values for most common a values. 0.005 0.01 0.02 0.03 0.04 0.05 0.06 0.1 2.575 2.33 2.05 1.88 1.75 1.645 1.555 1.28 2 2.81 2.575 2.33 2.17 2.05 1.96 1.88 1.645 Critical Value (s) = ? v (c) What is the test statistic? Use the correct sign for the test statistic and round your answer to 3 decimal places. Zest