Problem

Translate the statement into a confidence interval. Approximate the level of confidence. In a survey of 800 adults in a country, $68 \%$ think teaching is one of the most important jobs in the country today. The survey's margin of error is $\pm 4 \%$. The confidence interval for the proportion is (Round to three decimal places as needed.)

Solution

Step 1 :Translate the statement into a confidence interval. The question is asking for a confidence interval for the proportion of adults who think teaching is one of the most important jobs. The proportion is given as 68% and the margin of error is given as 4%.

Step 2 :The confidence interval can be calculated by adding and subtracting the margin of error from the proportion. The proportion is 0.68 and the margin of error is 0.04.

Step 3 :Calculate the lower bound of the confidence interval by subtracting the margin of error from the proportion: 0.68 - 0.04 = 0.64.

Step 4 :Calculate the upper bound of the confidence interval by adding the margin of error to the proportion: 0.68 + 0.04 = 0.72.

Step 5 :The confidence interval for the proportion of adults who think teaching is one of the most important jobs is between 0.64 and 0.72.

Step 6 :Final Answer: The confidence interval for the proportion is \(\boxed{(0.64, 0.72)}\).

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Source: https://solvelyapp.com/problems/19017/

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