A national caterer determined that 87% of the people who sampled their food said that it was delicious. A random sample of 144 people is obtained from a population of 5000. The 144 people are asked to sample the caterer's food. If sample proportion, P^, is the sample proportion saying that the food is delicious, what is the mean of the sampling distribution of the sample proportion, p^?
To determine the mean of the sampling distribution of the sample proportion, p^, you can use the formula:
Mean of p^ = P
Where P is the true proportion of the population.
In this case, the given information states that 87% of the people who sampled the food said it was delicious. Therefore, the true proportion of the population, P, is 0.87.
So, the mean of the sampling distribution of the sample proportion, p^, is 0.87.
To determine the mean of the sampling distribution of the sample proportion, you need to multiply the population proportion by the sample size.
In this case, the population proportion of people who said the food was delicious is 87% or 0.87, and the sample size is 144.
So, the mean of the sampling distribution of the sample proportion (p^) can be calculated as:
mean = population proportion x sample size
mean = 0.87 x 144
mean ≈ 125.28
Therefore, the mean of the sampling distribution of the sample proportion is approximately 125.28.