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 1,660 square feet while the median square footage of homes within the city limits is 1,240 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 20 houses and record the square footage of the homes using public records. Which of the following is true?
1) The shape of the sampling distribution of the mean square footage of homes will be right skewed.
2) The shape of the sampling distribution of the mean square footage of homes will be left skewed. Recall that if the mean is larger than the median, the distribution is right skewed. If the mean is less than the median, the distribution is left skewed. And if the mean is equal to the median, or if the sample size is greater than 30, the distribution will be approximately symmetric.
3) If the statistician sampled 15 more homes within the city limits and added their data to the original sample of 20 homes then the shape of the sampling distribution of the mean square footage of all 35 homes will be approximately symmetric. Recall that the Central Limit Theorem says that if the sample size is greater than 30, then the sampling distribution of the mean will be symmetric.
4) 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.
5) 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.