Question

a random sample of 715 adults is surveyed in order to investigate how common it is for people to check their email more than one time per day. researchers report that four out of every five surveyed adults check their email more than one time per day. ultimately, researchers plan to use this sample data to estimate the proportion of all adults who check their email more than one time per day. based on this information, which one of the following statements is most accurate?

the value of ( p ) is 0.80 because 80% of the sample said they check their email more than one time per day.

the value of ( hat{p} ) is 0.80 because this is the proportion that was calculated based on the sample of data.

both ( p ) and ( hat{p} ) are equal to 0.80 because a random sample is a good representation of the entire population.

the value of ( hat{p} ) is unknown because we are not given any information about the population size.

the value of ( p ) can be found by dividing the number of adults who say they check their email more than one time per day by 715.

Explanation:

Step1: Recall the definitions of \(p\) and \(\hat{p}\)

• \(p\) is the population proportion (unknown in this case as we are trying to estimate it from the sample).
• \(\hat{p}\) is the sample proportion.

Step2: Calculate the sample proportion

We are given that \(4\) out of \(5\) surveyed adults check their email more than once a day. So, \(\hat{p}=\frac{4}{5}= 0.80\). This value is calculated from the sample data.

Answer:

The value of \(\hat{p}\) is \(0.80\) because this is the proportion that was calculated based on the sample of data.