Question

The General Social Survey (GSS) is a survey of approximately 2000 adults conducted each year since 1972, for a total of 38,000 participants. During several years of the GSS, participants were asked how many close friends they have. The mean for this variable is 7.44 friends, with a standard deviation of 10.98. The median is 5.00, and the mode is 4.00.

4. Now pretend you randomly selected a sample of 80 people from this population. Using symbolic notation, calculate the mean and standard error of the distribution of means.

5.What is the likely shape of the distribution of means? Explain your answer

.6. Let’s pretend that the data represent the entire population. Imagine that you randomly selected one person from this population who reported that he had 18 close friends. Would you compare this person’s score to a distribution of scores or to a distribution of means? Explain your answer

Answer 1

4:

Here we have

Since sample size is large, that is greater than 30 so sampling distribution of sample mean will be approximately normal distribution with mean

and standard deviation is

5:

Since sample size is large, that is greater than 30 so sampling distribution of sample mean will be approximately normal distribution.

6:

Since we select only one person so its score should be compare to a distribution of scores.