Exercise 3.38 tells us that 206 of the 303 inductees to the Rock and Roll Hall of Fame have been performers. The data are given in Rock-and-Roll. Using all inductees as your population:

(a) Use StatKey or other technology to take many random samples of size \(n=10\) and compute the sample proportion that are performers. What is the standard error of the sample proportions? What is the value of the sample proportion farthest from the population proportion of \(p=0.68\) ? How far away is it?

(b) Repeat part (a) using samples of size \(n=20\).

(c) Repeat part (a) using samples of size \(n=50\).

(d) Use your answers to parts (a), (b), and (c) to comment on the effect of increasing the sample size on the accuracy of using a sample proportion to estimate the population proportion.

Data From Exercise 3.38:

From its founding through 2015, the Rock and Roll Hall of Fame has inducted 303 groups or individuals,
and 206 of the inductees have been performers while the rest have been related to the world of music in some way other than as a performer. The full dataset is available in Rock-and-Roll.