The GSS has asked subjects ‘How long [in years] have you lived in the city, town
ID: 3339732 • Letter: T
Question
The GSS has asked subjects ‘How long [in years] have you lived in the city, town or community where you live now?’ The responses of 1415 subjects in one survey had a [sample]…mean of 20.3 and a [sample] standard deviation of 18.2.”
a) Interpret the reported sample mean (state its meaning in words).
b) Compute a confidence interval for this estimate and interpret it. Be sure you are clear what your level of confidence is. Show work.
c) Suppose that the sample size was only 100 (instead of 1415). What would the confidence interval be now? Show work
Explanation / Answer
a) Interpret the reported sample mean (state its meaning in words).
This means that the mean of the years of those survey in the sample is 20.3
b) Compute a confidence interval for this estimate and interpret it. Be sure you are clear what your level of confidence is. Show work.
We know that the CI is given as
mean +-z*sd/sqrt(n), where n = 1415 , sd = 18.2 , mean = 20.3 and z = 1.96 for 95% CI
20.3 +- 1.96*18.2/sqrt(1415)
19.35,21.24
c) Suppose that the sample size was only 100 (instead of 1415). What would the confidence interval be now? Show work
We know that the CI is given as
mean +-z*sd/sqrt(n), where n = 100 , sd = 18.2 , mean = 20.3 and z = 1.96 for 95% CI
20.3 +- 1.96*18.2/sqrt(100)
16.73 ,23.86
as the sample size decreases the width of the confidence interval increases
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