A Sampling Distribution for Gender in the Rock and Roll Hall of Fame Exercise 3.37 tells us that 47 of the 303 inductees to the Rock and Roll Hall of Fame have been female or have included female members. 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 female or with female members. What is the standard error for these sample proportions? What is the value of the sample proportion farthest from the population proportion of \(p=0.155\) ? 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 3.37:

From its founding through 2015, the Rock and Roll Hall of Fame has inducted 303 groups or individuals. Forty-seven of the inductees have been female or have included female members. The full dataset is available in Rock-and-Roll