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Family Values In a USA Today/Gallup poll, 768 of 1024
Chapter 5, Problem 28AYU(choose chapter or problem)
In a USA Today/Gallup poll, 768 of 1024 randomly selected adult Americans aged 18 or older stated that a candidate’s positions on the issue of family value are extremely or very important in determining their vote for president.
(a) Obtain a point estimate for the proportion of adult Americans aged 18 or older for which the issue of family values is extremely or very important in determining their vote for president.
(b) Verify that the requirements for constructing a confidence interval for p are satisfied.
(c) Construct a 99% confidence interval for the proportion of adult Americans aged 18 or older for which the issue of family values is extremely or very important in determining their vote for president.
(d) Is it possible that the proportion of adult Americans aged 18 or older for which the issue of family values is extremely or very important in determining their vote for president is below 70%? Is this likely?
(e) Use the results of part (c) to construct a 99% confidence interval for the proportion of adult Americans aged 18 or older for which the issue of family values is not extremely or very important in determining their vote for president.
Questions & Answers
QUESTION:
In a USA Today/Gallup poll, 768 of 1024 randomly selected adult Americans aged 18 or older stated that a candidate’s positions on the issue of family value are extremely or very important in determining their vote for president.
(a) Obtain a point estimate for the proportion of adult Americans aged 18 or older for which the issue of family values is extremely or very important in determining their vote for president.
(b) Verify that the requirements for constructing a confidence interval for p are satisfied.
(c) Construct a 99% confidence interval for the proportion of adult Americans aged 18 or older for which the issue of family values is extremely or very important in determining their vote for president.
(d) Is it possible that the proportion of adult Americans aged 18 or older for which the issue of family values is extremely or very important in determining their vote for president is below 70%? Is this likely?
(e) Use the results of part (c) to construct a 99% confidence interval for the proportion of adult Americans aged 18 or older for which the issue of family values is not extremely or very important in determining their vote for president.
ANSWER:
Step 1 of 6
From the given information, 768 of 1024 randomly selected adult Americans aged 18 or older stated that a candidate’s positions on the issue of family value are extremely or very important in determining their vote for president.
a) The mean of the distribution of sample proportion is equal to the population proportion.
That is, \(\mu_{x}^{-}=\hat{p}\).
Here the given values are x = 768 and n = 1024.