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.

Answer 1

A C E are the statements which apply here.

Median is higher than mean which means that the data is right skewed.

Invalidating B statement and applying that the A statement is true.

Taking a higher amount of data would lead to normalisation. N is greater than 30 therefore there is normalisation and the data will be symmetric --- Reason for C

Reason for E ----A sample standard deviation is a statistic. This means that it is calculated from only some of the individuals in a population. Since the sample standard deviation depends upon the sample, it has greater variability. Thus the standard deviation of the sample is greater than that of the population.

Invalidating statement D