Question

The 2010 General Social Survey asked the question: "For how many days during the past 30 days was your mental health, which includes stress, depression, and problems with emotions, not good?" Based on responses from 1,151 US residents, the survey reported a 95% confidence interval of 3.40 to 4.24 days in 2010.

(a) Interpret this interval in context of the data.

The researchers can be 95% confident that the sample mean number of ''not good'' days in the past 30 is between 3.40 and 4.24

The researchers can be 95% confident that the true population mean number of ''not good'' days in the past 30 is between 3.40 and 4.24

95% of surveys will report a mean number of ''not good'' days in the past 30 is between 3.40 and 4.24

(b) Suppose the researchers think a 99% confidence level would be more appropriate for this interval. Will this new interval be smaller or larger than the 95% confidence interval?

smaller since we have less room for error

larger since the margin for error must be larger

smaller since we will be more sure of our results

larger since the standard error would be larger

(c) If a new survey were to be done with 500 Americans, would the standard error of the estimate be larger, smaller, or about the same. Assume the standard deviation has remained constant since 2010.

larger since we can be less sure of our estimate with a smaller sample size

smaller since we can collect more accurate results from fewer individuals

about the same since the standard deviation has remained constant, so we shouldn't expect different results

Answer 1

Explanation:

a) Interpretation of confidence interval

The researchers can be 95% confident that the true population mean number of ''not good'' days in the past 30 is between 3.40 and 4.24

b) When we increase confidence level from 95% to 99%

confidence interval becomes

larger since the margin for error must be larger

c) If sample size decreases from 1151 to 500,

the std error of the estimate would increase because std error is inversely proportion to square root of n.

larger since we can be less sure of our estimate with a smaller sample size