Question

7.1 Section Exercise Question 3 of 18 (1 point) Altempt 3 of Unlimited View questlon in a popup 7 A sample of size n 87 is drawn from a population whose standard deviation is a Part 1 of 2 (a) Find the margin of error for a 90% confidence interval for . Round the answer to at least three decimal places. The margin of error for a 90% confidence interval for u is Part 2 of 2 (b) If the sample size were n56, would the margin of error be larger or smaller? (Choose one) , because the sample size is (Choose one)

Answer 1

a. Given n = 87 and $\sigma$ = 7

Margin of error for a 90% confidence interval for Mu is given by $Z^{^{ *}}\frac{\sigma}{\sqrt{n}}$ z* = z score for 90% confidence level

Z* = 1.64

Margin of error = = 1.231

1.64 V87

b. If the sample size n = 56 then the margin of error will be larger because the sample size is smaller.

As the margin of error is inversely proportional to sample size then if sample size decreases then margin error will increase.

In this case margin error is = = 1.5341

1.64. 56