so234 ch 7

If you have a sample statistic and an unknown population standard deviation, you would use which formula to calculate the confidence interval. a. b. c. d. none of these choices are correct

b.

Calculate the confidence interval: The average age of the 1225 respondents was 25.3 with a standard deviation of 1.9.

25.3 ± 0.11 or the average age of the population is between 25.19 and 25.41.

In the formulas for constructing interval estimates based on sample proportions, the expression Pu (l - Pu) has a maximum value of... a. 0.50 b. 0.25 c. 1.00 d. 0.75

b. 0.25

An alpha level of 0.05 is the same as a confidence level of... a. 99.5% b. 95% c. 90.5% d. 90%

b. 95%

The most commonly used confidence level is... a. 99.5% b. 95% c. 90.5% d. 90%

b. 95%

A confidence level of 99% is the same as an alpha level of... a. 0.05 b. 0.10 c. 0.01 d. 0.001

c. 0.01

The width of an interval estimate can be controlled by... a. changing the confidence level. b. changing the alpha level. c. changing the sample size. d. Any of the above

d. Any of the above

According to a study reported in the text, Americans report that the happiest day of the year is... a. Christmas. b. Easter. c. The Fourth of July. d. Thanksgiving.

a. Christmas.

The efficiency of any estimator can be improved by... a. increasing the sample size. b. decreasing the sample size. c. making the sample representative. d. changing the sample.

a. increasing the sample size.

To increase the probability that a confidence interval will include the population parameter... a. lower the alpha level. b. raise the alpha level. c. increase the bias of the sample statistic. d. set efficiency to zero.

a. lower the alpha level.

We can estimate the probability that sample means and proportions lie within a given distance of the population value because these statistics are... a. unbiased. b. efficient. c. random. d. biased.

a. unbiased.

In estimation procedures, the Z score that corresponds to an alpha of .05 is... a. ± 1.96 b. ± 2.58 c. ± 3.78 d. ± 9.78

a. ± 1.96

Calculate the confidence interval: Of the 998 respondents questioned, 246 identified themselves as Catholic.

0.25 ± 0.03 or the percentage of the population which is Catholic is between 22% and 28%.

Calculate the confidence interval: The average number of children for the 945 respondents for which we have information was 1.98 with a standard deviationof 1.04.

1.98 ± .07 or the average number of children is between 1.91 and 2.05 per respondent.

Calculate the confidence interval: The average years of school completed for 734 respondents was 11.9 with a standard deviation of 0.5.

11.9 ± .04 or: The average number of years of school completed is between 11.86 and 11.94 years.

Two sample statistics are unbiased estimators. They are... a. means and proportions. b. means and standard deviations. c. medians and modes. d. proportions and percentages.

a. means and proportions.

In estimation procedures, as the alpha level decreases, the corresponding Z score... a. moves closer to the mean of the sampling distribution. b. moves away from the mean of the sampling distribution. c. becomes negative. d. becomes positive.

a. moves closer to the mean of the sampling distribution.

In estimation procedures, the alpha level is... a. the same as the confidence level. b. the parameter we are trying to estimate. c. always greater than the standard error. d. equal to the efficiency ratio minus the bias coefficient.

a. the same as the confidence level.

In constructing interval estimates based on sample proportions (Ps), the population proportion (Pu) must be estimated. It is most conservative to estimate Pu at... a. Ps b. .50 c. .25 d. 1.00

b. .50

The probability that a sample mean is within ± 1 Z of the population mean is about... a. 0.34. b. 0.68. c. 0.95. d. 0.99.

b. 0.68.

A random sample of 500 reports an average yearly income of $42,000 with a standard deviation of $1000. An estimateof the parameter at the 95% level is about $175 wide. In this research situation... a. the parameter is $42,000. b. the sample is unrepresentative. c. the alpha level is 0.05. d. the sample mean is $175.

c. the alpha level is 0.05.

According to the 2012 presidential election polls, most pollsters suggested... a. a significant win for Barack Obama. b. a slight win for Mitt Romney. c. too close to call. d. a significant win for Mitt Romney.

c. too close to call.

Sample proportions are... a. biased. b. theoretical. c. unbiased. d. none of these choices are correct.

c. unbiased.

A random sample of 200 includes 100 Protestants. The researcher estimates, at the 95% confidence level, that between43% and 57% of the population is Protestant. In this research situation... a. alpha is .10 b. Pu is 95 c. N is 100 d. Ps is .50

d. Ps is .50

Based on an EPSEM sample of 300 state university students, we estimate that the average number of hours of study time each week is 30 ± 2. In this example, the population is... a. the 300 state university students. b. all state university students. c. unknown. d. the same as the parameter.

b. all state university students.

As sample size increases, confidence interval width... a. increases. b. decreases. c. remains the same. d. changes proportionally.

b. decreases.

If the population parameter is not included in estimation, then... a. an interval estimate is wrong. b. an interval estimate is right. c. an interval estimate is right, but biased. d. an interval estimate is wrong, but biased.

a. an interval estimate is wrong.

All other things being equal, larger sample will cost more to process... a. but will not necessarily have narrower confidence intervals. b. and will always produce narrower confidence intervals. c. and will always produce wider confidence intervals. d. but will produce more precise intervals if the confidence level is low.

a. but will not necessarily have narrower confidence intervals.

Public opinion polls and election projections are examples of... a. estimation procedures. b. hypothesis testing. c. non-statistical research methods. d. blatant misuse of statistical procedures.

a. estimation procedures.

In estimation procedures, BLANK are estimated based on the value of BLANK. a. statistics, parameters b. parameters, statistics c. values, frequencies d. sample, populations

a. statistics, parameters

When using sample means as estimators, we usually estimate the population standard deviation with... a. the sample standard deviation. b. the sampling distribution standard deviation. c. the population parameter. d. the Z score.

a. the sample standard deviation.

In the formula for finding a confidence interval when the value of the population standard deviation is unknown, we change Nto N-1. The reason for this change is... a. to correct for the fact that s is biased. b. the standard deviation of a sample is always greater than the standard deviation of the population. c. the standard deviation of a sample is unbiased. d. sample size is much too large.

a. to correct for the fact that s is biased.

The sample standard deviation is a biased estimator of the population standard deviation. When using sample means as estimators, we correct for bias in the formula for finding confidence intervals by... a. using N - 1 rather than N. b. using N rather than N - 1. c. using s rather than Z. d. squaring the value of Z.

a. using N - 1 rather than N.

If a researcher changes from the 90% confidence level to the 95% level, the confidence interval will... a. widen. b. decrease in width. c. not be affected. d. widen only if N is greater than 100.

a. widen.

Sample size and the width of confidence intervals... a. increase at the same rate. b. increase at different rates: sample size increases faster than interval width. c. increase at different rates: sample size increases more slowly than interval width. d. have no relationship to each other.

b. increase at different rates: sample size increases faster than interval width.

As our confidence in an interval estimate increases, the width of the interval... a. decreases. b. increases. c. remains the same. d. increases or decreases depending on the alpha level.

b. increases.

To construct the narrowest possible confidence intervals, use BLANK. a. small samples b. large samples c. the least efficient estimator d. an unbiased statistic

b. large samples

To decrease the probability that a confidence interval will NOT include the population parameter... a. lower the alpha level. b. raise the alpha level. c. increase the bias of the sample statistic. d. set efficiency to zero.

b. raise the alpha level.

We have used an alpha of 0.01 to estimate the average hours of television viewing for residents in a retirement home. What is the chance that our interval estimate does not contain the true population mean? a. 99% b. 10% c. 1% d. 1/10 of 1%

c. 1%

Which sample size will produce the confidence interval with the smallest width? a. 100 b. 200 c. 500 d. 1000

d. 1000

A reputable poll will include in its description, at the very minimum, the... a. standard deviation. b. margin of error. c. standard error of the population. d. confidence intervals.

d. confidence intervals.

To calculate the confidence interval based on sample means, you need all but which of the following... a. sample mean. b. Z score determined by alpha level. c. standard error of the mean. d. standard deviation of the population.

d. standard deviation of the population.

In a two person race, if the Republican presidential candidate is projected to attract 44% ± 3% of the vote and theDemocratic candidate is projected to attract 46%±3% of the vote, then... a. the Republican is the probable winner. b. the Democrat is the probable winner. c. neither candidate will win a majority of votes in the electoral college. d. the race is "too close to call."

d. the race is "too close to call."

Calculate the confidence interval: Of the 1220 respondents for whom we have information, 178 said that they had been divorced at least once.

0.15 ± 0.03 or the percentage of the population that has been divorced is between 12% and 18%.

Four hundred and thirty two of the 668 respondents questioned said that they favored capital punishment for peopleconvicted of murder. Ten years ago, in response to the same question, 378 out of 703 people were in favor of capitalpunishment. Has support for capital punishment risen over the ten year period?

Now: 0.65 ± .04 or: The percentage of the population which supports capital punishment is between 61% and 69%. Ten years ago: 0.54 ± .04 or: The percentage of the population which supported capital punishment was between 50% and58%. The lower limit of the confidence interval for this year (61%) is higher than the upper limit of the confidence interval for tenyears ago (58%). It seems safe to conclude that support has increased over the ten year period.

A random sample of 500 reports an average yearly income of $42,000 with a standard deviation of $1000. An estimate of the parameter at the 95% level is about $175 wide. In this research situation... a. we can be 95% confident that the population mean is 42,000 ± 175. b. the sample size is much too small to justify the use of estimation procedures. c. the alpha level is 1000. d. the sample mean is $175.

a. we can be 95% confident that the population mean is 42,000 ± 175.

The probability that an interval estimate does not include the population value is called... a. the margin. b. alpha. c. an error. d. the odds.

b. alpha.

The larger the sample size (N), the... a. smaller the parameter. b. greater the efficiency. c. lower the bias. d. larger the standard error of the mean.

b. greater the efficiency.

The average weight of a sample of women who attend aerobics classes at the YWCA is 130 pounds. We construct a confidence interval (using an alpha of 0.05) of ± 3.45. The upper and lower limits of our estimate are... a. 130.00 and 133.45. b. 126.55 and 130.45. c. 126.55 and 133.45. d. unknown; these values will depend on the number of women who are truly serious about exercising.

c. 126.55 and 133.45.

The text reports a famous incident in which BLANK was incorrectly predicted to defeat BLANK. a. Kennedy, Nixon b. Nixon, Kennedy c. Dewey, Truman d. Reagan, Bush

c. Dewey, Truman

The sizes of four samples vary as follows: Sample A, N = 100 Sample B, N = 76 Sample C, N =1000 Sample D, N = 150 Which sample will produce the most efficient estimate? a. Sample A b. Sample B c. Sample C d. Sample D

c. Sample C

In the United States, based on the responses of a random sample to a survey, between 70% and 80% of the people who do the family grocery shopping are women. This is... a. not a finding which can be generalized. b. a biased estimate. c. a confidence interval estimate. d. sexism at its most offensive.

c. a confidence interval estimate.

Wider confidence intervals... a. are sure to include the population value. b. are less likely to include the population value. c. are more likely to include the population value. d. do not alter the chance of including the population value.

c. are more likely to include the population value.

An estimator is unbiased if the mean of its sampling distribution is equal to... a. the midpoint of the distribution. b. the sample mean. c. the population value. d. the population median.

c. the population value.

From a random sample of 300 students at a state university, you find the average number of hours of study time each week is 30 with a standard deviation of 5. In this research situation,... a. the sample is too small. b. the population consists of the 300 students surveyed. c. the sample is the 300 students surveyed. d. the parameter is 30.

c. the sample is the 300 students surveyed.

Based on an EPSEM sample of 300 state university students, we estimate that the average number of hours of study time each week is 30 ± 2. In this example, the parameter is... a. 300. b. 30. c. ± 2. d. unknown.

c. ± 2.

A random sample of 200 includes 100 Protestants. The researcher estimates, at the 95% confidence level that between43% and 57% of the population is Protestant. In this research situation... a. the parameter is 200 b. Pu is .43 or .57 c. N is 100 d. alpha is 0.05

d. alpha is 0.05

The efficiency of a sample estimator is essentially a matter of... a. accuracy. b. validity. c. centrality. d. dispersion.

d. dispersion.

The more efficient the estimate, the more the sampling distribution... a. is evenly spread from the mean to ± 2 standard deviations. b. becomes flatter. c. clusters to the right of the mean. d. is clustered around the mean.

d. is clustered around the mean.

In BLANK of the cases, the mean of a sample selected by EPSEM will be more than ± 3 Z's from the population mean. a. less than 1% b. more than 5% c. more than 90% d. more than 99%

d. more than 99%

The goal of estimation procedures is to infer BLANK from BLANK. a. intervals, estimates b. bias, efficiency c. statistics, parameters d. parameters, statistics

d. parameters, statistics

The greater the confidence level, the BLANK width of the confidence interval. a. narrower b. more representative c. more efficient d. wider

d. wider