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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 81 students and records their weekday mean sleep time as 6.80 hours. Assume that the population standard deviation is fairly stable at 1.60 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 2% for most common oz values. \"-- za 2.575 2.33 2.05 1.88 1.75 1.645 1.555 1.28 255 2.81 2.575 2.33 2.17 2.05 1.96 1.88 1.645 Fm. = C] 2 Round the margin of error and confidence interval values to 2 decimal places. Calculate the margin of error E = [3 What is the 95% confidence interval? [:jsiusl:] (b) If the researcher wants to be 97% confident that the sample mean is within 0.20 hours (or 12 min) of the true population mean weekday sleep time, how many students should he include in the sample? Fm. = C] 2 Round your answer (11) UP to the next whole number. The required sample size 'n. is [:J