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 the context of the data.

(b) What does “95% confidence” mean? Explain in the context of the application.

(c) 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?

Answer 1

The survey reported a 95% confidence interval of 3.40 to 4.24 days in 2010.

(a)

In context of the data, it means that we can say with 95% confidence that out of the last 30 days, the population mean number of days in which the mental health of US residents was not good was between 3.40 and 4.24 days.

(b)

95% confidence mean a level of significance of 5%. The level of significance is the probability of rejecting the null hypothesis when it in fact true. So 95% confidence interval would mean that we are 95% confident that the value of the true population parameter which is here the population mean number of days on which the mental health of US residents was not so good would lie within a certain interval, which in this context lies between 3.40 and 4.24 days. This interval or range of values can be taken by the true population parameter is what is the confidence interval.

(c)

If we use 99% confidence, our new interval would be larger. This is because to say we are 99% confident that the true population mean lies in a certain interval would mean that we have to increase the width of the interval to account for that extra confidence of 4%.

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