Question

"Should college tuition be free as long as the student maintains a 3.0 GPA?" describe 3 things you think a researcher can do to make the margin of error smaller (i.e., a narrower confidence interval). Be sure you provide an explanation with each item you identify.

Answer 1

Three things which can reduce the margin of error are reduced standard deviation, reduced confidence level and increased sample size.

Margin of error =

suppose z = 1.96 for 95% confidence level, s = 5 and n = 25

then, margin of error =

(A) reducing margin of error using confidence level

z = 1.64 for 90% confidence level

this implies

margin of error =

So, reducing the confidence level results in smaller margin of error

(B) reducing margin of error using standard deviation

let s = 2

this implies

margin of error =

=

= 0.784

So, reducing the standard deviation results in smaller margin of error

(C) reducing margin of error using sample size n

let n = 50

this implies

margin of error =

=

= 1.39

So, increasing the sample size n results in smaller margin of error