According to the U.S. Statistical Abstract, the proportion of new single-family houses completed in 2003 that had exactly three bedrooms was 0.51.
a. Is the variable for number of bedrooms being treated here as quantitative or categorical? Describe a way to treat it as the other type of variable.
b. The underlying distribution has just two possible values, 0 and 1. Sketch its probability histogram, and describe it as left-skewed, right-skewed, or close to symmetric.
c. If we took repeated random samples of 6 new single-family houses in 2003 and recorded the proportion of houses with exactly three bedrooms in each sample, what should be the mean of all these sample proportions?
d. What should be the standard deviation (to the nearest hundredth) of all sample proportions for samples of size 6?
e. Tell whether the shape of the distribution of sample proportions for samples of size 6 would be left-skewed, right-skewed, symmetric but not normal, or approximately normal. (Justify your answer.)
f. If we took repeated random samples of 24 new single-family houses in 2003 and recorded the proportion of houses with exactly three bedrooms in each sample, what should be the mean of all these sample proportions?
g. What should be the standard deviation (to the nearest hundredth) of all sample proportions for samples of size 24?
h. Tell whether the shape of the distribution of sample proportions for samples of size 24 would be left-skewed, right-skewed, fairly symmetric but not normal, or approximately normal. (Justify your answer.)