Deck 5: Using a Sample Mean or Proportion to Talk About a Population: Confidence Intervals

Question 1

Each "building block" in a sampling distribution of sample means is

A) a population mean
B) a sample mean
C) a set of sample means
D) the difference between the sample mean and the population mean

Answer 1

B

Question 2

It is common that a sample mean will not exactly equal the mean of the population from which the sample was drawn. This phenomenon is referred to as:

A) the standard error
B) the standard deviation
C) sampling error
D) sampling bias

Answer 2

C

Question 3

Jake takes many samples from a population, calculates the mean for each sample on a variable of interest, then places these means on a graph. The graph Jake has created is called:

A) a sample distribution
B) a mean distribution
C) a sampling distribution
D) a variation distribution

Answer 3

C

Question 4

According to the Central Limit Theorem, if you take decently sized samples from the highly skewed distribution:

A) the resulting sampling distribution likely will be skewed in the same direction as the original distribution
B) the resulting sampling distribution likely will be skewed in the opposite direction as the original distribution
C) the resulting sampling distribution likely will be multimodal
D) the resulting sampling distribution likely will be normal (bell-shaped)

Question 5

Gail takes many samples from a highly skewed distribution, and shows that the resulting sampling distribution is normally shaped (bell-shaped). Gail is illustrating a key aspect of:

A) inference
B) confidence intervals
C) the Central Limit Theorem
D) Chebyshev's Theorem

Question 6

What two pieces of information do you need to find the estimate of the standard error of the mean?

A) the sample standard deviation and the sample size
B) the sample size and the population size
C) the sample size and the population mean
D) the sample size and the number of samples

Question 7

With regard to a claim about a population mean, what is the correct order:

A) actual distance, number of standard errors, percentage probability
B) number of standard errors, actual distance, percentage probability
C) percentage probability, number of standard errors, actual distance
D) percentage probability, actual distance, number of standard errors

Question 8

Which of the following is the best interpretation of a 95% confidence interval?

A) 95% of the population is within the confidence interval.
B) We are 95% confident that the sample mean is accurate.
C) We are 95% confident that the population mean is within this interval.
D) There is a 5% chance that the population mean is within the interval.

Question 9

Which of the following is true?

A) The 95% confidence interval is always wider than the 99% confidence interval using the same sample statistics.
B) The 99% confidence interval is always wider than the 95% confidence interval using the same sample statistics.
C) The 95% confidence interval is sometimes the same width as the 99% confidence interval using the same sample statistics.
D) The 100% confidence interval is the best confidence interval.

Question 10

With regard to building a confidence interval, what is the correct order:

A) actual distance, number of standard errors, percentage probability
B) number of standard errors, actual distance, percentage probability
C) percentage probability, number of standard errors, actual distance
D) percentage probability, actual distance, number of standard errors

Question 11

In the 2008GSS, the 61 Hispanic respondents' average age at the birth of their first child was 22.95, with a sample standard deviation of 4.88. What is the 95% confidence interval for the population mean?

A) 21.69 ≤ μ ≤ 24.21
B) 21.90 ≤ μ ≤ 24.00
C) 21.50 ≤ μ ≤ 23.50
D) 18.07 ≤ μ ≤ 27.83

Question 12

A researcher finds that the 13 Muslims surveyed in the 2008GSS had a mean of 2.38 children with a standard deviation of 2.10. With this information, she builds a confidence interval for the Muslim population's number of children: 1.05 ≤ μ ≤ 3.71. Which confidence interval is she using?

A) 90%
B) 95%
C) 99%
D) 99.9%

Question 13

All other things being equal, a confidence interval based on a larger sample will be ________ a confidence interval based on a smaller sample.

A) wider than
B) narrower than
C) the same width as
D) worse than

Question 14

What two pieces of information do you need to find the estimate of the standard error of the proportion?

A) the sample proportion and the population proportion
B) the sample size and the sample proportion
C) the sample proportion and the sample standard deviation
D) the sample size and the population size

Question 15

All other things being equal, which proportion will produce the widest confidence interval?

A) .10
B) .30
C) .60
D) .80

Question 16

Of the 219 white GSS2008 respondents in their 20s, 63 of them claim the ability to speak a language other than English. With 99% confidence, what is the upper limit of the population proportion based on these statistics?

A) .29
B) .32
C) .35
D) .37

Question 17

Which proportion represents the largest amount of variation:

A) .25
B) .50
C) .65
D) .95

Question 18

If we are building a confidence interval, and our sample size is 25, how many degrees of freedom do we have?

A) 1
B) 23
C) 24
D) 25

Question 19

What media does Hughey study in his article on "magical negros"?

A) television dramas
B) comic books
C) archival photographs
D) films

Question 20

What method does Hughey use in his article on "magical negros"?

A) survey research
B) content analysis
C) chi-square
D) oversampling

Question 21

Brazil and Kirk's research on Uber studied what possible effect?

A) lessening rush hour
B) lessening drunk driving
C) lowering taxi rates
D) lowering road rage

Question 22

Brazil and Kirk found that Uber _______ overall fatalities.

A) dramatically lowered
B) slightly lowered
C) did not lower
D) actually raised

Question 23

According to Brazil and Kirk, an incidence rate ratio of 1 signifies:

A) your factor perfectly affects the outcome
B) your factor strongly affects the outcome
C) your factor weakly affects the outcome
D) your factor does not affect the outcome

Question 24

If race is coded white=1, black=2, other=3, which of the following Select Cases commands would not work to examine whites and blacks?

A) race=1 or race=2
B) race<3
C) race=1 and race=2
D) race<=2

Question 25

With regard to having SPSS select cases, the textbook warns you against:

A) deleting cases instead of selecting cases
B) using an "and" instead of an "or"
C) forgetting to get all your cases back
D) all of the above

Question 26

In a t-table, going across each row from left to right for any degree of freedom, the values increase, while at the top of the table, the probability decreases. Explain why this makes sense with regard to how a sampling distribution is set up.

Question 27

Someone claims that, for a particular situation on which they're working, the estimate of the standard error is 0. Explain what would have to be true for this to be the case.

Question 28

Explain, both mathematically and conceptually, why a larger sample size produces a smaller standard error.

Question 29

Explain, both mathematically and conceptually, why a large standard deviation produces a larger standard error.

Question 30

Someone claims that men who are attracted to their same sex are first attracted when they are 21 years old. Among the 28 men in the 2008GSS who say they are attracted to the same sex, the average age they say they were first attracted to the same sex is 16.82, with a standard deviation of 7.92. Given these statistics, is this claim possibly true?

Question 31

A friend comes to you and says he has learned how to build a 5% confidence interval. He is impressed by how precise it is. Explain to your friend why this newfound skill of his is not a good thing.

Question 32

Someone wants to try to build a confidence interval, but all of the cases in their sample have the exact same value on their variable of interest. Explain why their efforts to build a confidence interval will fail miserably.

Question 33

Someone wants to try to build a confidence interval, but they have only a single case in their sample. Explain why their efforts to build a confidence interval will fail miserably.

Question 34

Among the 232 GSS2008 respondents aged 66 and above, the mean number of times in the past year they visited a public library was 8.13 with a standard deviation of 23. Based on this information calculate a 95% confidence interval and full explain the results.

Question 35

According to the 2008 GSS, only 12 of the 28 GSS respondents aged 20-29 have health insurance. Build a 99% confidence interval with this sample information.