Question

In a survey, 31% of a randomly selected sample of n = 935 American adults said that they do not get enough sleep each night. The margin of error for the 95% confidence level was reported to be 3.2%. (a) Use the survey information to create a 95% confidence interval for the percentage that feels they don't get enough sleep every night_________%.(b) Do you think this sample could be used to estimate the percentage of college students who think they don't get enough sleep each night? Why or why not? A. Yes, the population the sample comes from is representative of college students, fulfilling the Fundamental Rule for Using Data For Inference B. No, the population the sample comes from may not be representative of college students, violating the Fundamental Rule for Using Data For Inference. O C. Yes, the population the sample comes from is representative of college students, violating the Fundamental Rule for Using Data For Inference. D. No, the population the sample comes from may not be representative of college students, fulfilling the Fundamental Rule for Using Data For Inference

Answer 1

a) [0.278; 0.342]

b) No, the population the sample comes from may not be representative of college students, violating the Fundamental Rule for Using Data For Inference.

Explanation:

Hello!

a)

The study variable is

X: Number of American adults that said that they do not get enough sleep each night.

The sample is n= 935 American Adults

Sample proportion 'p= 0.31

The margin of error of the 95% CI d= 0.032

The formula for a CI for the population proportion is:

['p ±
`Z_(1-\alpha /2)`*
`\sqrt{('p(1-'p))/(n) }`]

The basic structure of the CI formula is "Point estimator" ± "Margin of error"

So with the given data, you can calculate the CI.

[0.31 ± 0.032]

[0.278; 0.342]

So with a confidence level of 95%, you'd expect that the interval [0.278; 0.342] will contain the population proportion of the American adults that don't get enough sleep at night.

b)

The answer is no. The sample is of "American adults" there is no information on their education level, therefore it is possible that all of them have a college education or that none of the have. Since no further information about their education then you cannot be certain that this sample will be representative of the American College Students.

Then the correct option is B

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