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. 95% of surveys will report a 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 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 (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 standard error would be larger smaller since we will be more sure of our results larger since the margin for error must 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 about the same since the standard deviation has remained constant, so we shouldn't expect different results smaller since we can collect more accurate results from fewer individuals

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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4.12 Mental health: 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.

95% of surveys will report a 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 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

(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 standard error would be larger

smaller since we will be more sure of our results

larger since the margin for error must 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

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

smaller since we can collect more accurate results from fewer individuals

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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