6. The width of a confidence interval will be: A. Narrower for 99% confidence th

Question

6. The width of a confidence interval will be: A. Narrower for 99% confidence than 95% confidence B. Wider for a sample size of 100 than for a sample size of 50 C. Narrower for 90% confidence than 95% confidence D. Wider when the sample standard deviation (s) is small than when s is large 7. As standard deviation increases, samples size confidence A. Increases B. Decreases C. Remains the same to achi eve a specified level of 8. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n = 100 will be confidence interval for a population mean based on a sample ofn 50. A. Wider than B. Narrower than C. Equal to 9. When a confidence interval for a population proportion is constructed for a sample size n-30 and the value of p =.4, the interval is based on: A. The Z distribution B. The t distribution C. A Skewed distribution D. None of the above 10. In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a variance of .09. What is the 90% confidence interval for the true mean length of the bolt? A. 2.8355 to 3.1645 B. 2.5065 to 3.4935 C. 2.4420 to 3.5580 D. 2.8140 to 3.1860 E. 2.9442 to 3.0558 11. The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent (more than 90 days overdue). For this quarter, the auditing staff randomly selected 400 customer accounts and found that 80 of these accounts were delinquent. What is the 99% confidence interval for the proportion of all delinquent customer accounts at this manufacturing company? A. .1608 to .2392 B. .1992 to .2008 C. .1671 to 2329 D. .1485 to .2515 E. .1714 to.2286

Explanation / Answer

Question 6

Correct Answer: C. Narrower for 90% confidence than 95% confidence

Explanation:

We know that when we increase confidence level, interval becomes wider. When we increase sample size, interval becomes narrower. When sample standard deviation is large, interval becomes wider.

Question 7

Correct Answer: A. Increases

We know that we need to increase sample size when we increase standard deviation to achieve a specified level of confidence. For specified level of confidence, critical value will remain same. So maintaining same standard error, we need to increase sample size as per increment in standard deviation.

Question 8

Correct Answer: B. Narrower than

We know that when we increase sample size, interval becomes narrower.

Question 9

Correct Answer: A. The Z distribution.

We are given n=30, p = 0.4, so n*p = 30*0.4 = 12 and n*q = 30*0.6 = 18, so we can use Z distribution.

Question 10

We are given

n = 9,

Xbar = 3,

S^2 = 0.09,

So S = 0.3,

Confidence level = 90%

df = n – 1 = 8

Critical t value = 1.8595

(by using t-table)

Confidence interval = Xbar -/+t*S/sqrt(n)

Confidence interval = 3 -/+ 1.8595*0.3/sqrt(9)

Confidence interval = 3 -/+ 1.8595*0.3/3

Confidence interval = 3 -/+ 1.8595*0.1

Confidence interval = 3 -/+ 0.1860

Lower limit = 3 - 0.1860 = 2.8140

Upper limit = 3 + 0.1860 = 3.1860

Correct Answer: D. 2.8140 to 3.1860

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