Question

A young researcher takes a random sample of students enrolled at MSU and estimates the percent that are coffee drinkers to be 83%. The corresponding 95% confidence interval is given by (75.6%, 90.4%).

Approximately how many students did the researcher speak to in the process of creating this interval? Round your final answer to the nearest acceptable integer.

Answer 1

Solution,

Given that,

= 0.83

1 - = 1 - 0.83 = 0.17

margin of error = E = 0.904 - 0.83 = 0.074

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.96 / 0.074 )2 * 0.83 * 0.17

= 98.99

sample size = n = 99