Question

In each of Exercises 11.19-11.24, we have given a likely nange 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 $\hat{\beta }$to calculafe the required 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.

$0.7\text{or greater}$

Short answer

Part a) the educated guess is$0.7$
Part b), the observed values of the sample proportion that will yield larger margin of error is$0.3<\hat{p}<0.7$

Step-by-step solution

Step 1:Given information

$0.7\text{or greater}$

Step 2:Explaination Part a)

Identify the educated guess when the range is $0.7$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$0.7$in the range is closest to $0.5$Hence, educated guess $\left({\hat{p}}_g\right)$is $0.7$

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 larger than $0.3$but smaller than $0.7$, which provides the larger margin of error. Hence, the observed values of the sample proportion that will yield larger margin of error is$0.3<\hat{p}<0.7$.