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A recent findings reported that college students spend an average of 4.5 hours on social media...

A recent findings reported that college students spend an average of 4.5 hours on social media per person per day. The population standard deviation is 2.5 hours per day. A researcher took a random sample of 120 college students for making inferences about the population of college students. Answer the following questions about the sampling distribution of sample mean of number of hours on social media.

1) The mean of this sample of n=120 belongs to a sampling distribution. What is the shape of this sampling distribution?

2) What is the mean of all the sample means - the "Expected value of the Mean"?

3) What is the standard deviation of the sampling distribution?

4) If alpha = .05, and the sample mean was 5.2 hours per day on social media, was this an unusual sample - yes or no?

5) If the sample size were 25, what would the mean of the sampling distribution be?

Math   Statistics-And-Probability   
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Answer #1

(1) The shape of the sampling distribution is bell-shaped, just like a Normal distribution.
(2) The mean of all the sample mean = population mean = 4.5 hours.
(3) The standard deviation of the sampling distribution = population standard deviation/square root of sample size = = 0.2282.
(5) Even if the sample size changes, the mean of the sampling distribution will remain unchanged at 4.5 hours.

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