Question

In each of Exercises 11.19-11.24, we have given a likely range for the observed value of a sample proportion $\hat{p}$.

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

b. Ldentify 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.

$0.4\text{or greater}$

Short answer

Part a)educated guess $\left({\hat{p}}_g\right)$is $0.5$

Part b) the observed values of the sample proportion that will yield larger margin of error is none.

Step-by-step solution

Step 2:Given information

$0.4\text{or greater}$

Step 2:Explaination Part a)

Identify the educated guess when the range is $0.4$or greater.

Educated guess for $\hat{p}$can be identified by which the value in the range is closest to $0.5$Here, the value $0.5$in the range is closest to $0.5$. Hence, educated guess $\left({\hat{p}}_g\right)$is $0.5$

Step 2:Explaination Part b)

Identify the observed values of the sample proportion that will yield larger margin of error.

The observed value of $\hat{p}$had turned out to be $0.5$. Thus, there is no range for the observed values of the sample proportion that will yield larger margin of error. Hence, the observed values of the sample proportion that will yield larger margin of error is none.