5.28 Sleep time per night among college students was approximately normally distributed with mean µ = 6.78 hours and standard deviation σ = 1.24 hours. You plan to take an SRS of size n = 120 and compute the average total sleep time.
A) What is the standard deviation for the average time? Answer: 1.24/sq120 = 0.1132 hours
B) Use the 95 part of the 68-95-99.7 rule to describe the variability of this sample mean Answer: 6.78 +- 2(0.1132) = 6.55 to 7 hours
C) What is the probability that your average will be below 6.9 hours? Answer: Z-Score = (6.9 - 6.78)/0.1132 = 1.06. Conversion from Z table = 0.8554
5.29 Refer to the previous exercise. You want to use a sample size such that about 95% of the averages fall within + or - 5 minutes (0.08 hour) of the true mean µ = 6.78.
A) Based on your answer to part (b) in exercise 5.28, should the sample size be larger or smaller than 120?Larger
B) What standard deviation of x¯ do you need such that approximately 95% of all samples will have a mean within 5 minutes of µ? Unsure
C) Using the standard deviation you calculated in part (b), determine the number of students you need to sample.Unsure