Question

The Gallup-Healthways Well-being Index is a comprehensive survey of the health status of Americans.  A random sample of 2,580 adults were asked, "Have you ever been told by a physician or a nurse that you have depression?" Of these, 238 answered "Yes."

Using JMP construct the 99% confidence interval for the true proportion of Americans who have been told they have depression, and fill in the appropriate bounds in the confidence interval interpretation given below. Round your answers to two decimal places (i.e. 0._ _).

99% confident the true proportion of Americans who have been told by a physician or nurse they suffer from depression is between

and

Question 2 (1 point)

Refer to the scenario given in Question 1. According to the National Institute of Mental Health, 6.7% of adults suffer from depression. Is this percentage supported by the confidence interval found in Question1?

Question 2 options:

	Yes, because 6.7% does not fall in the confidence interval.
	There is not enough information given to make a determination.
	No, because 6.7% does not fall in the confidence interval.

Question 3 (1.5 points)

Question 3 options:

A study investigated ways to prevent staph infection in surgery patients. In a first step, researchers examined the nasal secretions of a random sample of 6,771 patients admited to various hospitals for surgery. They found that 1,251 of these patients tested positive for Staphylococcus aureus, a bacterium responsible for most staph infections.

Using JMP, find the 90% confidence interval for the true prorportion of patients admitted for surgery that tested positive for Staphylococcus aureus, and fill in the apporpriate bounds in the confidence interval interpretation given below. Round your answers to two decimal places (i.e. 0._ _).

90% confident the true proportion of patients admitted for surgery that tested positive for Staphylococcus aureus is between

and

Question 4 (1 point)

Saved

Refer to the scenario given in Question 3. Suppose a hospital does not have to implement any measures to control for staph infections if the percentage of patients who test positive for Staphylococcus aureus is less than 18%. Based on the confidence interval constructed in Question 3, does the hospital have to worry about controlling for staph infections?

Question 4 options:

	Yes, because the entire confidence interval is not below 18%.
	Yes, because 18% is in the confidence interval.
	There is not enough information to make a determination.

Answer 1

Q1: Sample, n = 2580

x = 238

Sample proportion, = 238/2580 = 0.0922

At =1-0.99 =0.01, two tailed critical value, = 2.58

9% confidence interval for the true proportion of Americans who have been told they have depression

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Q2: Answer: No, because 6.7% does not fall in the confidence interval.

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Q3: Sample, n = 6771

x = 1251

Sample proportion, = 1251/6771 = 0.1848

At =1-0.90 =0.10, two tailed critical value, = 1.645

90% confidence interval for the true proportion of Americans who have been told they have depression

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Q2: Answer: Yes, because 18% is in the confidence interval.