Question

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

$0.2orless$

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$0.2orless$

(b) The observed sample proportion values is $0.2<\hat{p}<0.8$.

Step-by-step solution

Part (a) Step 1: Given Information 

Given in the question that, the confidence interval is $0.2orless$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 guess is the value that is closest to the midpoint of the probable range of $0.2$or less.

As a result, the sample proportion is estimated to be $0.2$

Part (b) Step 1: Given Information 

Given in the question that, the confidence interval is $0.2orless$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 

The higher margin of error is found in the value range of $0.2-0.8$. As a result, the sample proportion observed values range from$0.2-0.8$. that is$0.2<\hat{p}<0.8$