# Quiz: Standard Deviation and Confidence Interval Estimate

**Topics:**Standard deviation, Sample size, Confidence interval

**Pages:**7 (973 words)

**Published:**February 13, 2011

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1Compute the critical value za/2 that corresponds to a 94% level of confidence.

A. 1.88

B. 1.66

C. 1.96

D. 2.33

2.In a sample of 10 randomly selected women, it was found that their mean height was 63.4 inches. Form previous studies, it is assumed that the standard deviation, σ, is 2.4. Construct the 95% confidence interval for the population mean.

A. (61.9, 64.9)

B. (58.1, 67.3)

C. (59.7, 66.5)

D. (60.8, 65.4)

3.Suppose a 95% confidence interval for µ turns out to be (120, 310). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width?

A. Increase the sample size.

B. Decrease the confidence level.

C. Increase the sample size and decrease the confidence level.

D. All of the choices will result in a reduced interval width.

4.A nurse at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 90% confidence that the true mean is within 4 ounces of the sample mean? The standard deviation of the birth weights is known to be 6 ounces.

A. 10

B. 9

C. 8

D. 7

5.Let t0 be a specific value of t. Find t0 such that the following statement is true:

P(t < t0) = 0.05 where df = 20)

A. -1.729

B. 1.729

C. -1.725

D. 1.725

6.When 335 college students were surveyed, 130 said they own their car. Find a point estimate for p, the population proportion of students who own their cars.

A. 0.285

B. 0.388

C. 0.612

D. 0.634

7.Many people think that a national lobby’s successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2250 who are in favor if gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 95% confidence interval.

A. .5625 ±0.0154

B. 0.123±0.0154

C. 0.133±0.0154

D. 0.111±0.0154

E. None of the above

8.A researcher in a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 3%.

A. 1841

B. 1842

C. 3683

D. 3684

9.Changing from a 95% confidence interval estimate for a proportion to a 99% confidence interval estimate, with all other thing being equal,

A. increases the interval size by 4%.

B. decreases the interval size by 4%.

C. increases the interval size by 31%.

D. decreases the interval size by 31%.

E. This question can not be answered without knowing the sample size.

10.In general, how does doubling the sample size chnge the confidence interval size?

A. Doubles the interval size

B. Halves the interval size

C. Multiplies the interval size by 1.414

D. Divided the interval size by 1.414

E. This question can not be answered without knowing the sample size.

11.A confidence interval estimate is determined from the GPAs of a simple random sample of n students. All other things being equal, which of the following will result in a smaller margin of error?

I. A smaller confidence level

II. A smaller sample standard deviation

III. A smaller sample size

A. I and II

B. I and III

C. II and III

D. I, II, and III

E. None of the above gives the complete set of true responses.

12.A survey was conducted to determine the percentage of high school students who planned to go to college. The results were stated as 82% with a margin of error of ±5%. What is meant by...

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