Question

Terrence randomly sampled 400 people and asked them if they prefer spring or fall. The results of his sample yielded an estimated population proportion of 43% who prefer spring. Deena randomly sampled 1,200 people and asked them if they prefer spring or fall. The results of her sample also yielded an estimated population proportion of 43% who prefer spring.

If Terrence and Deena use the same confidence level, which statement best describes the results of their margin of error calculations?

Terrence’s margin of error will be exactly three times as large as Deena’s.
Deena’s margin of error is half the amount of Terrence’s.
If Terrence samples 800 more people, his margin of error will be the same as Deena’s.
If Deena samples 400 fewer people, her margin of error would be exactly half the amount of Terrence’s.

Answer 1

on edge it's C. If Terrence samples 800 more people, his margin of error will be the same as Deena’s.

Answer 2

Explanation:

Margin of error is calculated as

Critical value multiplied by Std error of sample

= Critical value multiplied by square root of (variance/sample size)

Hence Margin of error

=
`z/t*((\sigma)/(√(n) ) )`

Thus square root of n is inversely proportion to margin of error.

Thus we have margin of error of Terrena would be square root of 3 times that of Deena

Thus option a, b and d are wrong

C is right because when sample sizes equal, the margin of error also would be equal.