Answer to Question #106784 in Statistics and Probability for Yusuf

Question

Consider the random variable X with a mean 100 and a population standard deviation of 9.
Assume a sample of size 30 was used.

Question 3
Which of the following statements is incorrect?
(1) When the sample size is 60 the 95% confidence interval estimate for the population mean is
.97:7227I 102:2773/:
(2) When the sample size is 100 the 95% confidence interval estimate for the population mean is
.98:2360I 101:7640/:
(3) When the sample size is 200 the 95% confidence interval estimate for the population mean is
.98:7527I 101:2473/:
(4) When the sample size is 500 the 95% confidence interval estimate for the population mean is
.99:2111I 100:7889/:
(5) None of the above.

Answer 1

X~(100,9²)

n=30

Question 3

CI=mean±(critical value) (SE of estimate)

For n=60

$=100±1.96*\frac {9}{\sqrt{60}}$

=(97. 7227,102.2773)

For n=100

$=100±1.96*\frac {9}{\sqrt{100}}$

=(98. 2360,101.7640)

For n=200

$=100±1.96*\frac {9}{\sqrt{200}}$

=(98. 7527,101.2473)

For n=500

$=100±1.96*\frac {9}{\sqrt{500}}$

=(99. 2111,100.7889)

Hence all statements are correct. Thus, the answer is (5) none of the above.