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Healthcare A Gallup poll conducted in November 2010 found
Chapter 5, Problem 30AYU(choose chapter or problem)
A Gallup poll conducted in November 2010 found that 493 of 1050 adult Americans believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.
(a) Obtain a point estimate for the proportion of adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.
(b) Verify that the requirements for constructing a confidence interval for p are satisfied.
(c) Construct a 95% confidence interval for the proportion of adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.
(d) Construct a 99% confidence interval for the proportion of adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.
(e) What is the effect of increasing the level of confidence on the width of the interval?
Questions & Answers
QUESTION:
A Gallup poll conducted in November 2010 found that 493 of 1050 adult Americans believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.
(a) Obtain a point estimate for the proportion of adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.
(b) Verify that the requirements for constructing a confidence interval for p are satisfied.
(c) Construct a 95% confidence interval for the proportion of adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.
(d) Construct a 99% confidence interval for the proportion of adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.
(e) What is the effect of increasing the level of confidence on the width of the interval?
ANSWER:Step 1 of 5
For the given information,a Gallup poll conducted in November 2010 found that 493 of 1050 adult Americans believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.
The mean of the distribution of sample proportion is equal to the population proportion.
That is ,\(\mu_{\bar{x}}=\widehat{p}\)
Here the given values are x=493 and n=1050.
Now, the sample proportion is
\(\widehat{p}=\frac{x}{n}=\frac{493}{1050}=0.4695\)
therefore ,\(\mu_{\bar{x}}=\widehat{p}=0.4695\) .