Question

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

$0.4to0.7$

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$0.4$

(b) The observed sample proportion values is$0.4<\hat{P}<0.7$

Step-by-step solution

Part (a) Step 1: Given Information  

Given in the question that, the confidence interval is $0.4-0.7$ 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 $0.4-0.7$dollars. As a result, $0.4$ is the educated estimation for the sample proportion.

Part (b) Step 1: Given Information  

Given in the question that, the confidence interval is $0.4-0.7$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 $0.4-0.7$. As a result, the observed sample proportion values vary from $0.4-0.7$. That is, $0.4<\hat{p}<0.7$.