Question

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

$0.7orless$

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$0.5$

(b) No sample proportion values have been detected.

Step-by-step solution

Part (a) Step 1: Given Information 

Given in the question that, the confidence interval is $0.7orless$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 $0.7orless$.

As a result, the sample proportion is estimated to be$0.5$

Part (b) Step 1: Given Information  

Given in the question that, the confidence interval is $0.7orless$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  

Does not result in a greater margin of error for the sample proportion of educated guesses in (a). As a result, no sample proportion values have been detected.