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In: Statistics and Probability

QUESTIONS 1 TO 4 ARE BASED ON THE FOLLOWING INFORMATION. Consider the random variable X with...

QUESTIONS 1 TO 4 ARE BASED ON THE FOLLOWING INFORMATION. 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 (97.2970; 102.7030)

(B) The 95% confidence interval estimate for the population mean is (96.7794; 103.2206)

(C) The 99% confidence interval estimate for the population mean is (95.7606; 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.

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 (97.7227; 102.2773)

(2) When the sample size is 100 the 95% confidence interval estimate for the population mean is (98.2360; 101.7640)

(3) When the sample size is 200 the 95% confidence interval estimate for the population mean is (98.7527; 101.2473)

(4) When the sample size is 500 the 95% confidence interval estimate for the population mean is (99.2111; 100.7889)

(5) None of the above.

Question 4

Assuming the level of significance stays the same, what happens to the confidence interval estimate when the sample size 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.

Expert Solution

orchestra answered 1 year ago

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