In a questionnaire, a random sample of commuters were asked whether it takes them more than 30 minutes to commute to work in the morning. The resulting confidence interval for the proportion of commuters who drive more than 30 minutes to work in the morning is is (0.27,0.51).

p'= 0.39

Step-by-step explanation:

Hello!

There was a random sample of 30 commuters taken and the time it took them to get to work was registered. Using this information a CI for the proportion of commuters that take more than 30 minutes to get to work was calculated.

The general structure for the CI for the population proportion is:

"point estimate" ± "margin of error"

The point estimate of the population proportion is the sample proportion and the margin of error corresponds to the semiamplitude of the interval. This means that the CI is centered in the sample proportion and you "subtract" and "add" the semiamplitude to it.

To know the value of the sample proportion of a given interval you have to find the value in the center of the interval doing the following calculation:

"Upperbond + Lowerbond" = 0.51 + 0.27 = 0.39

                     2                                 2

The sample proportion of the commuters that take more than 30min to get to work is p'= 0.39

I hope it helps!

oof

step-by-step explanation:

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