Question

According to a social media​ blog, time spent on a certain social networking website has a mean of 19 minutes per visit. Assume that time spent on the social networking site per visit is normally distributed and that the standard deviation is 44 minutes. Complete parts​ (a) through​ (d) below

a. If you select a random sample of 25 ​sessions, what is the probability that the sample mean is between 18.5 and 19.5 ​minutes?

b. If you select a random sample of 25 ​sessions, what is the probability that the sample mean is between 18 and 19 ​minutes?

c. If you select a random sample of 100 ​sessions, what is the probability that the sample mean is between 18.5 and 19.5 ​minutes?

Explain the difference in the results of​ (a) and​ (c).

c. The sample size in​ (c) is greater than the sample size in​ (a), so the standard error of the mean​ (or the standard deviation of the sampling​ distribution) in​ (c) is

less or greater than in​ (a). As the standard error decreases/increases values become more concentrated around the mean.​ Therefore, the probability that the sample mean will fall in a region that includes the population mean will always decrease/increase when the sample size increases.

Answer 1

The sample size in (c) is greater than the sample size in (a), so the standard error of the mean (or the standard deviation of the sampling distribution) in (c) is than in (a). As the standard error values become more concentrated around the mean. Therefore, the probability that the sample mean will fall in a region that includes the population means will always when the sample size increases.