Question

A sports analyst wants to estimate the true proportion of baseball players in the National League...

A sports analyst wants to estimate the true proportion of baseball players in the National League with a batting average of 0.400 or greater. They want to be 98% confident with a margin of error of 5%. How many players should be sampled if:

1. No prior estimate of p is available?
2. A previous study estimated that the proportion was 24%?

solution:

the given information as follows:

margin of error E = 5% = 0.05

confidence level = 98% = 0.98

so significance level = = 1-0.98 = 0.02

critical value of z =

a) if prior estimate p is not available

we assume = 0.5 is prior estimate is not available to find the requisite sample size.

so formula for margin of error is

so required sample size = 543 players, if prior estimate of p is not available

b)

if prior estimate of p is 24%

so = 0.24

since we cant take sample in fraction so the required sample size would be 397 players.