Deck 6: Estimation Procedures for Sample Means and Proportions

Question 1

Which of the following is estimated by a confidence interval?

A) sample size
B) population size
C) sample distribution
D) population value

Answer 1

population value

Question 2

Which of the following could be a valid margin of error value?

A) 0.25%
B) 4%
C) 44%
D) Any value could be a valid value for a margin of error.

Answer 2

Any value could be a valid value for a margin of error.

Question 3

Someone claims that "between 25% and 33% of Canadians spend more than $600 dollars on gifts during the December holiday shopping season." What type of statement is this?

A) a point estimate
B) an interval estimate
C) a biased estimate
D) an efficient estimate

Answer 3

an interval estimate

Question 4

What does it mean for an estimate to be unbiased?

A) The sampling distribution is clustered around its mean.
B) The sampling distribution has a small standard error.
C) The mean of its sampling distribution is equal to the population value of interest.
D) It has no margin of error.

Question 5

Which of the following is an unbiased estimate of a population parameter?

A) a sample mean from a non-random sample
B) a confidence interval from a non-random sample
C) a sample standard deviation from a random sample
D) a sample proportion from a random sample

Question 6

What is the probability that a sample mean is within ±1 Z of the population mean?

A) about 0.99
B) about 0.95
C) about 0.68
D) about 0.34

Question 7

In what proportion of cases will the mean of a sample selected by EPSEM be more than ±3 Z scores from the population mean?

A) less than 1%
B) between 3% and 5%
C) between 85% and 90%
D) between 95% and 99%

Question 8

A public health researcher wants to have high efficiency in estimating the population prevalence of Alzheimer's disease using a random sample of adults. Which of these samples would best accomplish this goal?

A) a sample of size 1,000
B) a sample of size 1,050
C) a sample of size 1,080
D) All samples would be equally efficient, so long as they are simple random samples.

Question 9

Why are large (i.e., efficient) random samples often desirable when attempting to estimate a population value?

A) Very efficient samples allow us to know the population standard deviation (ó).
B) Very efficient samples increase the confidence interval.
C) Greater efficiency reduces sample bias.
D) Greater efficiency reduces the standard error of the mean ( ).

Question 10

How is the standard deviation of a sampling distribution related to the size of the sample?

A) There is an inverse association: the bigger the n, the smaller the
B) There is a one-to-one association: the bigger the n, the bigger the
C) The bigger the n, the bigger the , but only if n is smaller than 100.
D) n and are independent of one another.

Question 11

A researcher draws a random sample of 220 dog owners in Alberta and finds that the mean number of veterinary visits per year is 3.3, with a standard deviation of 1.5. What would be a valid point estimate of the average number of visits for this population?

A) 220
B) 3.3 ± 1.5 standard deviations
C) 3.3
D) 1.5

Question 12

A researcher wants to estimate the number of living grandparents among young persons in Spain. Which of the following alphas (á) would be most strict (i.e., least tolerant of error) for constructing an interval estimate?

A) á = 0.01
B) á = 0.05
C) á = 0.10
D) á = 0.50

Question 13

What á value corresponds with a confidence level of 99%?

A) á = 0.001
B) á = 0.01
C) á = 0.05
D) á = 0.99

Question 14

In estimation procedures, which Z score corresponds to an alpha of 0.05?

A) ±1.96
B) ±2.58
C) ±3.78
D) ±9.78

Question 15

Researchers calculate a 95% confidence interval for the proportion of left-handed Canadian university students as 0.11 ± 0.4. On the basis of this estimation, what is the probability that the actual proportion of left-handed Canadian university students is below 0.07 or greater than 0.15?

A) 0.005
B) 0.025
C) 0.05
D) 0.25

Question 16

The random sample of a mean is = 50. The population standard deviation (ó) is 2.5. What is the 95% confidence interval?

A) c. i. = 50 ± 1.65(2.5) = 45.88 to 54.13
B) c. i. = 50 ± 1.96(2.5) = 45.10 to 54.90
C) c. i. = 50 ± 2.58(2.5) = 43.55 to 56.45
D)c) i. = 50 ± 3.29(2.5) = 41.78 to 58.23

Question 17

A researcher wishes to construct confidence intervals for a mean with a small random sample (N = 40). What must she assume?

A) The distribution of the population is normal.
B) The distribution of the sample is identical to the distribution of the population.
C) The standard deviation of the population is no bigger than 2× the size of the mean.
D) The size of the population is at least twice the size of the sample.

Question 18

The average weight of a sample of women who attended aerobics classes at the YMCA-YWCA was 130 pounds. A researcher constructed a confidence interval (using an alpha of 0.05) of ±3.45. Which of these pairs presents the lower and upper limits of the estimate?

A) 126.55 and 130.45
B) 126.55 and 133.45
C) 130.00 and 130.00
D) 130.00 and 133.45

Question 19

What is usually used to estimate the population standard deviation when using sample means as estimators?

A) the Z score
B) the sampling distribution standard deviation
C) the population parameter
D) the sample standard deviation

Question 20

What would be the appropriate sampling distribution for constructing confidence intervals of the average number of television sets in Canadian homes, where the population standard deviation is unknown?

A) chi distribution
B) alpha distribution
C) t distribution
D) Z distribution

Question 21

Which t distribution most resembles the Z distribution?

A) t distribution (df = 1.96)
B) t distribution (df = 38)
C) t distribution (df = 130)
D) All t distributions have an identical form.

Question 22

We are constructing confidence intervals for the mean number of women employed in software companies. We have a random sample of 30 companies, and the population's standard deviation is unknown. What would be the correct degrees of freedom for constructing the confidence intervals?

A) 30
B) 29
C) 15
D) 1

Question 23

What graphical tool is used to depict confidence intervals?

A) histogram
B) degrees of freedom graph
C) line chart
D) error bar graph

Question 24

Which of the following provides the most conservative estimate of P_u?

A) P_s
B) 0.25
C) 0.50
D) 1.00

Question 25

What will happen to the confidence interval if we change it from the 99% confidence level to the 95% level?

A) It will narrow.
B) It will widen.
C) It will remain the same.
D) It will widen only if the sample size exceeds 120.

Question 26

A research teams wishes to estimate the interval of ì with a sample of size 200. Without altering their sample size, what must the researchers do to obtain a very narrow confidence interval?

A) They must accept a relatively high probability of error for their estimate.
B) They must be willing to accept low precision in their estimate.
C) They must use a very low á value for their estimate.
D) They must use a very large Z score in their calculation.

Question 27

Describe what three changes must be made when constructing confidence intervals when the standard deviation of the population is estimated from s compared to when ó is known.

Question 28

Of the 700 respondents of a random sample, 89 said they were retired.

Question 29

Of the 668 respondents, 432 said that they are concerned about the environment. Ten years ago, in response to the same question, 378 of 703 respondents expressed concern for the environment.
Has environmental concern risen over the 10-year period?