Would appreciate help on 5.29 Parts B and C. Thank you very much!
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 x̄ 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
B) The standard deviation of x̄ do you need such that approximately 95% of all... View the full answer