Test Bank

Chapter 8: Point Estimates and Confidence Intervals

Multiple Choice

1. The uncertainty introduced into a statistic by the fact that any sample that is drawn is one of infinite samples that could have been drawn and that a sample statistic is therefore not necessarily equal to the population parameters is the definition of ______.

A. sampling error

B. standard error

C. standard distribution

D. sampling probability

2. A range of values that span a point estimate that is calculated so as to have a certain probability of containing the population parameter is called a ______.

A. probability interval

B. confidence interval

C. confidence percentage

D. point estimate of the confidence

3. The level of confidence is defined as ______.

A. the amount of confidence a researcher has in knowing the raw data sample statistic is equal to the point estimate interval

B. the probability that the level of confidence is set at .99, or 99%

C. the probability that a confidence interval contains the population parameter

D. the probability that the level of confidence is set at .95, or 95%

4. It is common practice among those in the scientific fields to set confidence levels at ______.

A. .5 (50%)

B. 1.00 (100%)

C. 0.68 (68%) or 0.75 (75%)

D. 0.95 (95%) or 0.99 (99%)

5. Confidence levels are set ______.

A. a priori; prior to the construction of the confidence interval

B. after the confidence interval is constructed

C. simultaneously to the construction of the confidence interval

D. after the statistical analysis has produced a few initial results

6. A two-tailed test is ______.

A. a statistical test in which the confidence level is split into thirds and placed into the two tails of the z distribution during the analytical phase of research

B. a statistical operation in which the confidence interval is widened to allow for the entire z distribution to be used by the researcher

C. a statistical test in which α is split in half and placed into both tails of the z or t distribution

D. a statistical technique in which the confidence level is doubled and placed into the two halves of the z or t distribution

7. What is a critical value?

A. the value of the confidence interval used to determine the confidence range

B. the value of z or t associated with a given α level

C. the value of the confidence level used to calculate the confidence interval

D. the value of z associated with a specific level of β and Δ

8. The fact that every sample that is drawn, and every sample that could potentially be drawn, has its own unique set of descriptive statistics, is called ______.

A. sampling error

B. magnitude of the error

C. sample distributional error

D. sritical error

9. What prevents a researcher from positing direct inferences from a sample to a population?

A. the confidence level associated with establishing the α level at a value too high for sample data

B. the confidence level associated with the distribution of raw scores

C. the variation in sample statistics such as means and proportions

D. the confidence level associated with establishing an α level at a value too low for sample data

10. A sample statistic, such as a mean or proportion that is used to estimate a population parameter, is referred to as what?

A. a point estimate

B. a critical value

C. the α level

D. the modal category midpoint

11. What acts as a sort of “bubble” that introduces flexibility into the estimate of the population parameter?

A. a critical inference level

B. a confidence interval

C. a critical value associated with the t distribution

D. the midpoint of the magnitudes

12. What happens when a researcher increases the confidence level?

A. The prediction becomes less precise.

B. The prediction becomes more precise.

C. Nothing happens.

D. The associated α level must be decreased to account for the added precision of the increased confidence level.

13. A researcher has decided upon an α level of α = .05. Based on this, what is the chance that the confidence level the researcher calculates will not include the true population parameter?

A. 95%

B. 5%

C. .05%

D. α = .05 has no bearing on the chances of making an error

14. A researcher has decided upon an α level of α = .01. Based on this, what is the chance that the confidence level the researcher calculates will include the true population parameter?

A. 1%

B. 95%

C. 5%

D. 99%

15. If a researcher had N = 120, which distribution would be used to construct a confidence interval?

A. z

B. t

C. χ²

D. N

16. Z_α represents what in statistics?

A. the confidence interval for proportions

B. the confidence level for proportions

C. the probability that the confidence interval does not contain the true population parameter

D. the probability that the confidence level does contain the actual population parameter

17. Confidence intervals are two-tailed because ______.

A. The z distribution is a bimodal distribution.

B. The t distribution is bimodal, having two modes.

C. The normal curve is bimodal, having two modes.

D. The normal curve has two halves that are divided by the mean.

18. Two-tailed tests have ______.

A. two critical values; one positive and one negative

B. one critical value

C. two critical values located in the positive tail

D. one critical value located in the negative tail

19. The absolute values of the critical values in a two-tailed confidence interval are the same because ______.

A. the normal curve is a bimodal distribution, with each modal category having similar standard errors

B. the normal curve is symmetrical, and the z values in each half are identical to one another

C. the z distribution is a bimodal construct with one mode positive and the other negative

D. the absolute values of the critical values in a two-tailed confidence interval are not the same, this is a trick question.

20. If a confidence level is 95%, what is the corresponding z score?

A. ±2.58

B. ±1.96

C. ±0.95

D. ±0.05

21. If a confidence level is 99%, what is the corresponding z score?

A. ±2.58

B. ±1.96

C. ±0.99

D. ±0.05

22. Which distribution is used to construct confidence intervals for means when N ≤ 99?

A. the t distribution

B. the z distribution

C. Any distribution is sufficient when constructing confidence intervals.

D. the sampling distribution

23. What distribution is used to construct confidence intervals with proportions?

A. the population distribution

B. the z distribution

C. the t distribution

D. any of the above distributions would be fine to use

24. The term df’ symbolizes what in the determination of a confidence interval with a small sample?

A. degrees of freedom

B. determinant of freedom

C. determination of freedom

D. determination formula

25. In the t distribution, df is related to ______.

A. the z distribution’s unimodal nature

B. the z distribution's symmetrical nature

C. sample size

D. the bimodal characteristics of the t distribution

26. A statistical test in which α is split in half and placed into both tails of the z or t distribution is called a ______.

A. one-tailed test

B. two-tailed test

C. three-tailed test

D. none of these

27. In the calculations for a confidence level involving a small sample, the acronym “df” stands for ______.

A. degrees of freedom

B. degrees of friction

C. degrees of function

D. none of these

28. Because of ______, a sample proportion cannot be assumed to equal the population proportion.

A. population error

B. rounding error

C. sampling error

D. none of these

29. The symbol ______ is used to denote a sample proportion in calculations for a confidence interval involving proportions.

A.

B. x

C. SD

D. df

30. In the calculation for a confidence interval involving proportions, the population proportion is symbolized by ______.

A. P

B. p

C. Prop.

D.

31. In social science research, the two most common α levels used with large samples are ______ and ______.

A. .10; .15

B. .01; .02

C. .05; .10

D. .01; .05

32. When trying to determine the critical value for t, it is first necessary to calculate the ______.

A. standard deviation

B. range

C. degrees of freedom

D. none of these

33. ______ are a way for researchers to use sample statistics to form conclusions about the probable values of population parameters.

A. standard deviations

B. parameters

C. confidence intervals

D. none of these

34. When deciding on what confidence intervals to use, it is important to remember that as confidence increases, the precision of the estimate ______.

A. increases

B. decreases

C. remains the same

D. none of these

35. There must be at least ______ successes and ______ failures in the sample in order to construct a confidence interval on the basis of proportions.

A. 1; 1

B. 2; 2

C. 4; 4

D. 5; 5

1. The variation in sample statistics such as means and proportions precludes direct inference from a sample to a population.

2. It is much more likely that an estimate of the value of a population parameter is accurate when the estimate is a range of values rather than one single value.

3. Confidence levels are commonly set at .95 or .99 when working with large samples.

4. It is relatively common for researchers to establish their level of confidence at 1.00, or 100%, as a time-saving tactic designed to increase reliability and validity.

5. The α level itself is never used in the formula for the confidence interval. It is simply used to help determine the critical value.

6. It can be assumed that a mean or standard deviation in a sample is an exact match to the mean or standard deviation in the population because often sample statistics are very similar, if not identical, to their corresponding population parameters.

7. A 99% confidence level would produce a confidence interval that has a greater chance than a 95% confidence level of being correct but would be wider and less precise.

8. In calculations for a confidence interval involving proportions, it is a reasonably safe bet that the z distribution can be used as long as the sample is large and contains at least five successes and at least five failures.

9. In calculations for a confidence interval involving proportions, there is really no statistical difference between the population proportion, P, and the sample proportion,. It’s simply a matter of two words designed to describe the same thing.

10. In the construction of confidence intervals, the choice of the level of confidence is up to the discretion of the researcher.

11. Confidence intervals for proportions make use of the t distribution, regardless of sample size.

12. The z distribution is always used with confidence intervals for proportion.

13. α is the probability that the confidence interval will not contain the true population parameter.

14. Z_α represents the probability that the confidence interval does not contain the actual population parameter.

15. Confidence levels are established after the construction of the confidence intervals.

16. A sample statistic such as a mean or proportion is also referred to as a point estimate in the field of statistics.

17. A range of values spanning a point estimate that is calculated so as to have a certain probability of containing the population parameter is the confidence interval.

18. The probability that the confidence interval contains the population parameter is called the level of confidence.

19. The probability that a confidence interval does not contain the true population parameter is represented by the Greek symbol x.

20. The value of z or t associated with a given α level is referred to as a parameter.

1. If a researcher has a 95% confidence level, what is the chance that the confidence interval will not contain the population parameter?

2. What is the reasoning behind the use of a two-tailed test in a research project?

3. Explain why a researcher would not wish to set their level of confidence at 100%.

4. For the formula below identify the various components, , Z_α, S, and N.

5. A researcher has a data set of homicides occurring in large Southern metropolitan areas consisting of 304 cases with a mean of 25.68 and a standard deviation of 11.26. The researcher has established α = .05. Calculate the resulting confidence interval for this set of data.