The Universal Music Group is the music industry leader worldwide in sales according to Nielsen Sound Scan. Suppose a researcher wants to determine what market share the company holds in the city of St. Louis by randomly selecting 1,003 people who purchased a CD last month. In addition, suppose 25.5% of the purchases made by these people were for products manufactured and distributed by the Universal Music Group.
a. Based on these data, construct a 99% confidence interval to estimate the proportion of the CD sales market in St. Louis that is held by the Universal Music Group.
b. Suppose that the survey had been taken with 10,000 people. Re-compute the confidence interval and compare your results with the first confidence interval.
How did they differ? What might you conclude from this about sample size and confidence intervals?