One of the questions asked of a random sample of adult Americans on the 2004 Gen
ID: 3048777 • Letter: O
Question
One of the questions asked of a random sample of adult Americans on the 2004 General Social Survey (GSS) was:
From time to time, most people discuss important matters with other people. Looking back over the last six months— who are the people with whom you discussed matters important to you? Just tell me their first names or initials.
The interviewer then recorded how many names each person gave. The GSS is a survey of a representative sample of U.S. adults who are not institutionalized. There were 1467 responses, and the average number of close friends reported was 1.987, with a standard deviation of 1.771. The data are not strongly skewed.
1. Explain how you know from the sample average and sample standard deviation that the distribution of number of close friends people tend to report is not bell-shaped.
a. The sample standard deviation is very small compared to the mean
b. The sample standard deviation is very large compared to the mean
2. It is valid to use the theory-based (t-distribution) approach to find a confidence interval. True or False?
3. A theory-based inference applet was used to find a 99% confidence interval of (1.8977, 2.1063). Based on the confidence interval alone, is there evidence that the average number of close friends people tend to report is different from 2? How are you deciding?
a. Yes, because 2 is not in the interval
b. Yes, because 2 is in the interval
c. No, because 2 is not in the interval
d. No, because 2 is in the interval
Explanation / Answer
1) option B is correct
b. The sample standard deviation is very large compared to the mean
2) true as sample size is very large.,
3)
d. No, because 2 is in the interval
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