Question

we have given a likely range for the observed value of a sample proportion $\hat{P}$

$0.2to0.4$

a. Based on the given range, identify the educated guess that should be used for the observed value of $\hat{p}$to calculate the required sample size for a prescribed confidence level and margin of error.

b. Identify the observed values of the sample proportion that will yield a larger margin of error than the one specified if the educated guess is used for the sample-size computation.

Short answer

(a)The sample proportion is estimated to be 0.2.

(b)The observed values of the sample proportion is$0.2<\hat{p}<0.4$

Step-by-step solution

Part (a) Step 1: Given Information 

Given in the question that, the confidence interval is$0.2-0.4$we have to identify the educated guess that should be used for the observed value of $\hat{p}$to calculate the required sample size for a prescribed confidence level and margin of error.

Part (a) Step 2: Explanation 

The educated prediction is the value that is closest to the midpoint of the expected range of $0.2-0.4$dollars. As a result, $0.2$is the educated estimation for the sample proportion.

Part (b) Step 1: Given Information 

Given in the question that, the confidence interval is$0.2-0.4$we have to

Identify the observed values of the sample proportion that will yield a larger margin of error than the one specified if the educated guess is used for the sample-size computation.

Part (b) Step 2: Explanation 

A bigger margin of error is provided by the value range of $0.2-0.4$. As a result, the observed sample proportion values vary from $0.2-0.4$. That is,$0.2<\hat{p}<0.4$.