Question: A random survey of 300 geography students on the St. George campus and 100 geography students on the U of T Scarborough campus were recently conducted. 45 of the St. George campus students and 10 of the Scarborough campus students reported that they were enrolled as part-time students.

(a) Can the sampling distribution of difference of proportions \({{\hat{p}}_{1}}-{{\hat{p}}_{2}}\) be approximated by a normal distribution? Show your calculations.

(b) Is the proportion of part-time students at St. George significantly different from the proportion of part-time students at Scarborough? Use the critical value approach, with α = 0.05.

(c) Construct a 99% confidence interval to estimate the difference between the proportions. Does this confidence interval support your results from part b? Explain.

HINT: In part c), be sure not do any ‘radical’ rounding off. If one of your intermediate steps involves a small number, e.g., 0.00005478, round this to the first non-zero digit, e.g., 0.00005.