Answer to Question #106783 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 1
Consider the statements below.
(A) The 90% confidence interval estimate for the population mean is .97:2970I 102:7030/:
(B) The 95% confidence interval estimate for the population mean is .96:7794I 103:2206/:
(C) The 99% confidence interval estimate for the population mean is .95:7606I 104:2394/:
Which statement(s) are correct?
(1) Only A.
(2) Only B.
(3) Only C.
(4) Only A and B.
(5) A, B and C.

Question 2
Assuming the sample size stays the same, what happens to the confidence interval estimate when
the level of confidence increases?
(1) The confidence interval estimate doesn’t change.
(2) The confidence interval estimate becomes wider.
(3) The confidence interval estimate becomes narrower.
(4) The confidence interval estimate converges to zero.
(5) None of the above.

Answer 1

X~N(100,92)

n=30

Question 1

(5) A,B and C are correct.

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

For 90% confidence interval,

$=100±(1.6449)*(\frac {9} {\sqrt {30 }})$

=(97. 270,102.7030)

For 95% confidence interval,

$=100±(1.64)∗( \frac {9} {\sqrt {30 } })$

=(96. 7794,103.2206)

For 99% confidence interval,

=$100±(2.58)*(\frac {9} {\sqrt {30 }})$

=(95. 7606,104.2394)

Question 2

When the sample size remains constant the confidence interval estimate becomes wider as the confidence interval increases.

(2) The confidence interval estimate becomes wider.