A national caterer determined that 37% of the people who sampled their food said that it was delicious. Arandom sample of 144 people is obtained from a population of 5000. The 144 people are asked to sample the^catererʹs food. If p is the sample proportion saying that the food is delicious, what is the standard deviation of^the sampling distribution of p?
A) 0.04
B) 0.002
C) 0.48
D) 0.23

Question

Quizplus · Accepted Answer

The standard deviation of the sampling distribution of $p$ (the sample proportion) is calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, where $p = 0.37$ (the proportion of people who said the food was delicious) and $n = 144$ (the sample size). Plugging in these values, we get $\sqrt{\frac{0.37(1-0.37)}{144}} = \sqrt{\frac{0.37(0.63)}{144}} = \sqrt{\frac{0.2331}{144}} = \sqrt{0.00161875} \approx 0.04$.

A National Caterer Determined That 37% of the People Who