Look at the following sampling distribution of sample means. This sampling distr

Question

Look at the following sampling distribution of sample means. This sampling distribution came from census data from math 140 students in the fall 2015 semester and describes the number of 6) hours of sleep per night. Use the sampling distribution to answer the following questions 6.4 6.7 68 6.9 7.0 7.1 7.2 6,31 a) What is the shape of the sampling distribution? b) The center of the distribution is at 6.751 hours of sleep per night Would this be a good appraximation of the population mean average amount of sleep for math 140 students in fall 20157 (Yes or No) c) There area total of 400 dots. To estimate the standard error, we need find the middle 95% of 400 dots. What is 9S% of 4007 d) We want to approximate the middle 95% of the dots. How many dots should we count in from the left and right tal in order to estimate middle 95% of dots?

Explanation / Answer

(a) Shape of sampling distribution is approximately normal.

(b) Yes, the mean of 6.751 hours sleep is a good approximation.

(c) 95% of 400 are 380 so we will calculate values between 10 to 390.

(d) we wil cound 10 dots from each side to calculate middle 95% population.

(e) In left side the 10th dot comes at 6.42 and 390th dot comes at 7.08

so 95 % confidence interval (6.42, 7.08)

(f) the difference between these two values is 4 times of standard error for the distribution

4 * = 7.08 - 6.42

= 0.165 hours

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