According to the U.S. Statistical Abstract, the proportion of new single-family houses completed in 2003 that had two or more stories was 0.53.
a. Is the variable for number of stories being treated here as quantitative or categorical?
b. The underlying distribution has just two possible values, 0 and 1. Sketch its probability histogram, and describe it as left-skewed, right-skewed, fairly symmetric but not normal, or normal.
c. If we took repeated random samples of 4 new single-family houses in 2003 and recorded the proportion of houses with two or more stories 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 4?
e. Tell whether the shape of the distribution of sample proportions for samples of size 4 would be left-skewed, right-skewed, symmetric but not normal, or approximately normal. (Justify your answer.)
f. If we took repeated random samples of 50 new single-family houses in 2003 and recorded the proportion of houses with two or more stories 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 50?
h. Tell whether the shape of the distribution of sample proportions for samples of size 50 would be left-skewed, right-skewed, fairly symmetric but not normal, or approximately normal. (Justify your answer.)