Problem

Let $p$ be the population proportion for the following condition. Find the point estimates for $p$ and $q$.
A study of 4564 adults from country A, 3086 think mainstream media is more interested in making money than in telling the truth.
The point estimate for $p, \hat{p}$, is (Round to three decimal placeshs needed.)

Answer

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Answer

Final Answer: The point estimates for $p$ and $q$ are $\boxed{0.676}$ and $\boxed{0.324}$ respectively.

Steps

Step 1 :Let $p$ be the population proportion for the following condition. Find the point estimates for $p$ and $q$.

Step 2 :A study of 4564 adults from country A, 3086 think mainstream media is more interested in making money than in telling the truth.

Step 3 :The point estimate for $p$, denoted as $\hat{p}$, is the sample proportion. In this case, it is the proportion of adults from country A who think mainstream media is more interested in making money than in telling the truth. This can be calculated by dividing the number of adults who think this way (3086) by the total number of adults surveyed (4564).

Step 4 :The point estimate for $q$, denoted as $\hat{q}$, is the complement of $\hat{p}$, which is 1 - $\hat{p}$.

Step 5 :Calculate $\hat{p}$: $\hat{p}$ = 3086 / 4564 = 0.6761612620508326

Step 6 :Calculate $\hat{q}$: $\hat{q}$ = 1 - $\hat{p}$ = 0.3238387379491674

Step 7 :Final Answer: The point estimates for $p$ and $q$ are $\boxed{0.676}$ and $\boxed{0.324}$ respectively.

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