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. (b) What does "95% confident" 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? (d) 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.

Question

Araceli Whitehead

Mathematics

9 March, 06:19

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. (b) What does "95% confident" 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? (d) 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.

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Answers (2)

Know the Answer?

Delilah Dickson · Answer 1

The answer is d because it would stay constant due to the number of surveys and answers recorded.

Reece Perkins · Answer 2

a) In 30 days, 95% of the population sufferred mental health problems for 3.4 to 4.24 days.

b) 95% confidence means that if the research is repeated, we can be 95% sure that mean number of days will fall between 3.4 to 4.24 days

c) larger

d) smaller

Step-by-step explanation:

Confidence interval refers to the extent of having same results if the investigation is re-taken. A greater confidence interval means that larger obervations are taken into account. Hence range increases.

The larger the sample size, the smaller is the standard deviation