Question

The city government has collected data on the square footage of houses within the city. They found that the average square footage of homes within the city limit is 1,240 square feet while the median square footage of homes within the city limits is 1,660 square feet. The city government also found that the standard deviation of home square footage within the city limits is 198 square feet. A statistician hired by a local home-carpeting company is going to randomly select a sample of 24 houses and record the square footage of the homes using public records. Which of the following is true?

Select all that apply.

Select one or more:

a. The shape of the sampling distribution of the mean square footage of homes will be right skewed.

b. The shape of the sampling distribution of the mean square footage of homes will be left skewed.

c. If the statistician sampled 11 more homes within the city limits and added their data to the original sample of 24 homes then the shape of the sampling distribution of the mean square footage of all 35 homes will be approximately symmetric.

d. The sampling distribution of the mean square footage will have a smaller standard deviation when compared to the standard deviation of square footage among all homes within the city limits.

e. The sampling distribution of the mean square footage will have a standard deviation equal to or larger than the standard deviation of square footage among all homes within the city limits.

I said that answers B and D are correct, however it was only marked as partially correct. Please tell me what answers are correct and which ones are incorrect. Thanks

Answer 1

The median is greater than mean for all houses in the population so distribution of square footage of homes within the city limits is skewed to left. It is not symmetric.

The sample size is 24 which is less than 30 so we cannot apply central limit theorem. The sampling distribution of sample mean will follow population distribution although it will be less skewed than population distribution. When the sample size is 35 then we can apply central limit theorem so sampling distribution of sample mean will be approximately normal.

The standard deviation of sampling distribution will be

Correct options are:

b. The shape of the sampling distribution of the mean square footage of homes will be left skewed.

c. If the statistician sampled 11 more homes within the city limits and added their data to the original sample of 24 homes then the shape of the sampling distribution of the mean square footage of all 35 homes will be approximately symmetric.

d. The sampling distribution of the mean square footage will have a smaller standard deviation when compared to the standard deviation of square footage among all homes within the city limits.