Question

According to a social media​ blog, time spent on a certain social networking website has a mean of 20 minutes per visit. Assume that time spent on the social networking site per visit is normally distributed and that the standard deviation is 6 minutes. Complete parts​ (a) through​ (d) below.

a. If you select a random sample of 16 ​sessions, what is the probability that the sample mean is between 19.5 and 20.5 ​minutes? ​(Round to three decimal places as​ needed.)

b. If you select a random sample of 16 ​sessions, what is the probability that the sample mean is between 19 and 20 ​minutes? ​(Round to three decimal places as​ needed.)

c. If you select a random sample of 100 ​sessions, what is the probability that the sample mean is between 19.5 and 20.5 ​minutes? ​(Round to three decimal places as​ needed.)

d. Explain the difference in the results of​ (a) and​ (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 or 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 or increase when the sample size increases.

Answer 1

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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 than in (a). As the standard error ▼ decreases, 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 ▼ increase when the sample size increases.