Question

A simple random sample of size n is drawn. The sample? mean,x is found to be 17.6 and the sample standard? deviation, s, is found to be

4.1

(a) Construct a 95% confidence interval about ? if the sample size, n, is 34

The confidence interval is?

(b) Construct a 95% confidence interval about ? if the sample size, n, is 61

The confidence interval is (?,?)

(use ascending order. Round to two decimal places as needed)

How does increasing the sample size affect the margin of error, E?

a. The margin of error increases.

b. The margin of error decreases

c. The margin of error does not change.

Answer 1

(A) we have

degree of freedom = n-1 = 34-1 = 33

t critical value using student's t distribution table at 0.05 significance level is t = 2.03

Confidence interval =

setting the given values, we get

Confidence interval =

this gives

Confidence interval =

(B) we have

degree of freedom = n-1 = 61-1 = 60

t critical value using student's t distribution table at 0.05 significance level is t = 2.00

Confidence interval =

setting the given values, we get

Confidence interval =

this gives

Confidence interval =

(C) We can see that the confidence interval width when sample size is 34, is more than the confidence interval width when sample size is 61. This means that the margin of eror decreasing with increase in the sample size

so, option B is correct