Transcript t - dpeasesummithilltoppers

AP Statistics Jeopardy
Normally
Random
Biometric
Regression
Relational
Design
100
100
100
100
100
100
200
200
200
200
200
200
300
300
300
300
300
300
400
400
400
400
400
400
500
500
500
500
500
500
600
600
600
600
600
600
Final Jeopardy
Probability
Signif. Tests
Sample
Tests
Anything
Inferred
Normally Random - 100
In a population of students, the number of calculators owned
is a random variable X with
P(X = 0) = 0.2, P(X = 1) = 0.6, and P(X = 2) = 0.2.
The mean of this probability distribution is
(a) 0.
(b) 2.
(c) 1.
(d) 0.5.
(e) The answer cannot be computed from the information
given.
Answer
Normally Random - 200
In a population of students, the number of
calculators owned is a random variable X with
P(X = 0) = 0.2, P(X = 1) = 0.6, and P(X = 2) = 0.2.
The variance of this probability distribution is
(a) 1.
(b) 0.63.
(c) 0.5.
(d) 0.4.
(e) The answer cannot be computed from the information
given.
Answer
Normally Random - 300
A smooth curve which approximates the shape of a
histogram and describes the overall pattern of a
distribution is called
(a)
(b)
(c)
(d)
(e)
a stemplot
a Normal probability plot
a destiny curve
a density curve
none of the above
Answer
Normally Random - 400
The following graph is a Normal
probability plot for the amount of rainfall
(in acre-feet) obtained from 26 randomly
selected clouds that were seeded with silver
oxide. Which of the following statements
about the shape of the rainfall distribution
is true?
(a) The distribution is Normal.
(b) The distribution is approximately
Normal.
(c) The distribution is roughly symmetric.
(d) The distribution has no potential outliers.
(e) The distribution is skewed.
Answer
Normally Random - 500
The distribution of the heights of students in a large class
is roughly Normal. Moreover, the average height is
68 inches, and approximately 95% of the heights are
between 62 and 74 inches. Thus, the standard
deviation of the height distribution is approximately
equal to
(a) 2
(d) 9
(b) 3
(e) 12
Answer
(c) 6
Normally Random - 600
If a store runs out of advertised material during a sale, customers
become upset, and the store loses not only the sale but also
goodwill. From past experience, a music store finds that the
mean number of CDs sold in a sale is 845, the variance is 225,
and a histogram of the demand is approximately Normal. The
manager is willing to accept a 2.5% chance that a CD will be
sold out. About how many CDs should the manager order for an
upcoming sale?
(a) 1295
(d) 875
(b) 1070
(e) 860
Answer
(c) 935
Normally Random - 100 Answer
In a population of students, the number of calculators owned
is a random variable X with
P(X = 0) = 0.2, P(X = 1) = 0.6, and P(X = 2) = 0.2.
The mean of this probability distribution is
(a) 0.
(b) 2.
(c) 1.
(d) 0.5.
(e) The answer cannot be computed from the information
given.
Normally Random - 200 Answer
In a population of students, the number of
calculators owned is a random variable X with
P(X = 0) = 0.2, P(X = 1) = 0.6, and P(X = 2) = 0.2.
The variance of this probability distribution is
(a) 1.
(b) 0.63.
(c) 0.5.
(d) 0.4.
(e) The answer cannot be computed from the information
given.
Normally Random - 300 Answer
A smooth curve which approximates the shape of a
histogram and describes the overall pattern of a
distribution is called
(a)
(b)
(c)
(d)
(e)
a stemplot
a Normal probability plot
a destiny curve
a density curve
none of the above
Normally Random - 400 Answer
The following graph is a Normal
probability plot for the amount of rainfall
(in acre-feet) obtained from 26 randomly
selected clouds that were seeded with silver
oxide. Which of the following statements
about the shape of the rainfall distribution
is true?
(a) The distribution is Normal.
(b) The distribution is approximately
Normal.
(c) The distribution is roughly symmetric.
(d) The distribution has no potential outliers.
(e) The distribution is skewed.
Normally Random - 500 Answer
The distribution of the heights of students in a large class
is roughly Normal. Moreover, the average height is
68 inches, and approximately 95% of the heights are
between 62 and 74 inches. Thus, the standard
deviation of the height distribution is approximately
equal to
(a) 2
(d) 9
(b) 3
(e) 12
(c) 6
Normally Random - 600 Answer
If a store runs out of advertised material during a sale, customers
become upset, and the store loses not only the sale but also
goodwill. From past experience, a music store finds that the
mean number of CDs sold in a sale is 845, the variance is 225,
and a histogram of the demand is approximately Normal. The
manager is willing to accept a 2.5% chance that a CD will be
sold out. About how many CDs should the manager order for an
upcoming sale?
(a) 1295
(d) 875
(b) 1070
(e) 860
(c) 935
Biometric Regression - 100
The following are resistant:
(a)
(b)
(c)
(d)
(e)
Least-squares regression line
Correlation coefficient
Both (a) and (b)
Neither (a) nor (b)
It depends
Answer
Biometric Regression - 200
In a large population of college students, 20% of the students
have experienced feelings of math anxiety. If you take a
random sample of 10 students from this population, the
probability that exactly 2 students have experienced math
anxiety is
(a) 0.3020.
(c) 0.2013.
(e)
1.
(b) 0.2634.
(d) 0.5.
Answer
Biometric Regression - 300
A basketball player makes 70% of her free throws. She takes
7 free throws in a game. If the shots are independent of each
other, the probability that she makes the first 5 and misses
the last 2 is about
(a) 0.635.
(b) 0.318.
(c) 0.015.
(d) 0.49.
(e) 0.35.
Answer
Biometric Regression - 400
One concern about the depletion of the ozone layer is that the increase in
ultraviolet (UV) light will decrease crop yields. An experiment was
conducted in a green house where soybean plants were exposed to varying
levels of UV, measured in Dobson units. At the end of the experiment the
yield (kg) was measured. The least-squares regression line is the line that
(a) minimizes the sum of the squared differences between the actual UV
values and the predicted UV values.
(b) minimizes the sum of the squared residuals between the actual yield and
the predicted yield.
(c) minimizes the sum of the squared differences between the actual yield
and the predicted UV.
(d) minimizes the sum of the squared residuals between the actual UV
reading and the predicted UV reading.
(e) minimizes the total variation in the data.
Answer
Biometric Regression - 500
One concern about the depletion of the ozone layer is that the increase in
ultraviolet (UV) light will decrease crop yields. An experiment was
conducted in a green house where soybean plants were exposed to varying
levels of UV, measured in Dobson units. At the end of the experiment the
yield (kg) was measured. A regression analysis was performed with the
following results:
Which of the following
is correct?
(a) If the UV reading increases by 1 Dobson unit, the yield is expected to
increase by 0.0463 kg.
(b) If the yield increases by 1 kg, the UV reading is expected to decline by
0.0463 Dobson units.
(c) The estimated yield is 3.98 kg when the UV reading is 0 Dobson units.
(d) The predicted yield is 4.3 kg when the UV reading is 20 Dobson units.
(e) None of these
Answer
Biometric Regression - 600
Mr. Nerdly asked the students in his AP
Statistics class to report their overall GPAs
and their SAT Math scores. The scatterplot
below provides information about his
students’ data. The dark line is the LSRL
for the data, and its equation is
y=270.45+109.42x. Which of the
following statements about the highlighted
point is FALSE?
(a) This student has a GPA of 2.9 and an SAT Math score of 670.
(b) If we used the LSL to predict this student’s SAT Math score, we would
make a prediction that is too low.
(c) This student’s residual is –82.23.
(d) Removing this data point would cause the correlation coefficient to
increase.
(e) Removing this student’s data point would increase the slope of the LSL.
Answer
Biometric Regression - 100
Answer
The following are resistant:
(a) Least-squares regression line
(b) Correlation coefficient
(c) Both (a) and (b)
(d) Neither (a) nor (b)
(e) It depends
Biometric Regression - 200
Answer
In a large population of college students, 20% of the students
have experienced feelings of math anxiety. If you take a
random sample of 10 students from this population, the
probability that exactly 2 students have experienced math
anxiety is
(a) 0.3020.
(c) 0.2013.
(e)
1.
(b) 0.2634.
(d) 0.5.
Biometric Regression - 300
Answer
A basketball player makes 70% of her free throws. She takes
7 free throws in a game. If the shots are independent of each
other, the probability that she makes the first 5 and misses
the last 2 is about
(a) 0.635.
(b) 0.318.
(c) 0.015.
(d) 0.49.
(e) 0.35.
Biometric Regression - 400
Answer
One concern about the depletion of the ozone layer is that the increase in
ultraviolet (UV) light will decrease crop yields. An experiment was
conducted in a green house where soybean plants were exposed to varying
levels of UV, measured in Dobson units. At the end of the experiment the
yield (kg) was measured. The least-squares regression line is the line that
(a) minimizes the sum of the squared differences between the actual UV
values and the predicted UV values.
(b) minimizes the sum of the squared residuals between the actual yield
and the predicted yield.
(c) minimizes the sum of the squared differences between the actual yield
and the predicted UV.
(d) minimizes the sum of the squared residuals between the actual UV
reading and the predicted UV reading.
(e) minimizes the total variation in the data.
Biometric Regression - 500
Answer
One concern about the depletion of the ozone layer is that the increase in
ultraviolet (UV) light will decrease crop yields. An experiment was
conducted in a green house where soybean plants were exposed to varying
levels of UV, measured in Dobson units. At the end of the experiment the
yield (kg) was measured. A regression analysis was performed with the
following results:
Which of the following
is correct?
(a) If the UV reading increases by 1 Dobson unit, the yield is expected to
increase by 0.0463 kg.
(b) If the yield increases by 1 kg, the UV reading is expected to decline by
0.0463 Dobson units.
(c) The estimated yield is 3.98 kg when the UV reading is 0 Dobson units.
(d) The predicted yield is 4.3 kg when the UV reading is 20 Dobson units.
(e) None of these
Biometric Regression - 600
Answer
Mr. Nerdly asked the students in his AP
Statistics class to report their overall GPAs
and their SAT Math scores. The scatterplot
below provides information about his
students’ data. The dark line is the LSRL
for the data, and its equation is
y=270.45+109.42x. Which of the
following statements about the highlighted
point is FALSE?
(a) This student has a GPA of 2.9 and an SAT Math score of 670.
(b) If we used the LSL to predict this student’s SAT Math score, we would
make a prediction that is too low.
(c) This student’s residual is –82.23.
(d) Removing this data point would cause the correlation coefficient to
increase.
(e) Removing this student’s data point would increase the slope of the LSL.
Relational Design - 100
The percent of cars listed in the
table with 4-cylinder engines that
are made in Germany is
(a)
(b)
(c)
(d)
(e)
10.5%.
21%.
50%.
80%.
91%.
Answer
Relational Design - 200
From the table we might conclude that
(a) there is clearly no relation between
country of origin and # of cylinders.
(b) the correlation between country of
origin and # of cylinders is likely to be
about 0.5.
(c) a regression line fitted to these data
would probably have a negative slope.
(d) there is evidence of some relation
between country of origin and number
of cylinders.
(e) the United States has far more cars than
any of the other countries.
Answer
Relational Design - 300
Control groups are used in experiments in order to
(a) control the effects of outside variables on the outcome.
(b) control the subjects of a study to ensure that all participate
equally.
(c) guarantee that someone other than the investigators, who have
a vested interest in the outcome, controls how the
experiment is conducted.
(d) achieve a proper and uniform level of randomization.
(e) None of the above.
Answer
Relational Design - 400
What electrical changes occur in muscles as they get tired?
Student subjects hold their arms above their shoulders as long
as they can. Meanwhile, the electrical activity in their arm
muscles is measured. This is:
(a) an observational study.
(b) an uncontrolled experiment.
(c) a randomized comparative experiment.
(d) a matched pairs design.
(e) impossible to describe unless more details of the study are
provided.
Answer
Relational Design - 500
The Community Intervention Trial for Smoking Cessation (COMMIT)
asked whether a community-wide advertising campaign would reduce
smoking. The researchers located 11 pairs of communities that were
similar in location, size, economic status, and so on. One community
in each pair participated in the advertising campaign and the other did
not. This is
(a) an observational study.
(b) a matched pairs experiment.
(c) a completely randomized experiment.
(d) a block design.
(e) impossible to answer unless more details of the study are provided.
Answer
Relational Design - 600
The following two-way table categorizes suicides committed in a particular year by
the sex of the victim and the method used.
Method
Firearms
Poison
Hanging
Other
Male
13,959
3,148
3,222
1,457
Female
2,641
2,469
709
690
Answer
Which of the following statements is consistent with the table?
(a) There is absolutely no evidence of a relation between the sex of the victim and the method
of suicide used.
(b) More women commit suicide than men.
(c) Men display a greater tendency to use firearms to commit suicide than do women.
(d) The correlation between method of suicide and sex of the victim is clearly positive.
(e) Females prefer poison over any other method of committing suicide.
Relational Design - 100 Answer
The percent of cars listed in the
table with 4-cylinder engines that
are made in Germany is
(a)
(b)
(c)
(d)
(e)
10.5%.
21%.
50%.
80%.
91%.
Relational Design - 200 Answer
From the table we might conclude that
(a) there is clearly no relation between
country of origin and # of cylinders.
(b) the correlation between country of
origin and # of cylinders is likely to be
about 0.5.
(c) a regression line fitted to these data
would probably have a negative slope.
(d) there is evidence of some relation
between country of origin and
number of cylinders.
(e) the United States has far more cars than
any of the other countries.
Relational Design - 300 Answer
Control groups are used in experiments in order to
(a) control the effects of outside variables on the outcome.
(b) control the subjects of a study to ensure that all participate
equally.
(c) guarantee that someone other than the investigators, who have
a vested interest in the outcome, controls how the
experiment is conducted.
(d) achieve a proper and uniform level of randomization.
(e) None of the above.
Relational Design - 400 Answer
What electrical changes occur in muscles as they get tired?
Student subjects hold their arms above their shoulders as long
as they can. Meanwhile, the electrical activity in their arm
muscles is measured. This is:
(a) an observational study.
(b) an uncontrolled experiment.
(c) a randomized comparative experiment.
(d) a matched pairs design.
(e) impossible to describe unless more details of the study are
provided.
Relational Design - 500 Answer
The Community Intervention Trial for Smoking Cessation (COMMIT)
asked whether a community-wide advertising campaign would reduce
smoking. The researchers located 11 pairs of communities that were
similar in location, size, economic status, and so on. One community
in each pair participated in the advertising campaign and the other did
not. This is
(a) an observational study.
(b) a matched pairs experiment.
(c) a completely randomized experiment.
(d) a block design.
(e) impossible to answer unless more details of the study are provided.
Relational Design- 600 Answer
The following two-way table categorizes suicides committed in a particular year by
the sex of the victim and the method used.
Method
Firearms
Poison
Hanging
Other
Male
13,959
3,148
3,222
1,457
Female
2,641
2,469
709
690
Which of the following statements is consistent with the table?
(a) There is absolutely no evidence of a relation between the sex of the victim and the method
of suicide used.
(b) More women commit suicide than men.
(c) Men display a greater tendency to use firearms to commit suicide than do women.
(d) The correlation between method of suicide and sex of the victim is clearly positive.
(e) Females prefer poison over any other method of committing suicide.
Probability Sign. Tests - 100
A randomly selected student is asked to respond Yes, No, or
Maybe to the question “Do you intend to vote in the next
presidential election?” The sample space is { Yes, No,
Maybe }. Which of the following represents a legitimate
assignment of probabilities for this sample space?
(a)
(b)
(c)
(d)
(e)
0.4, 0.4, 0.2
0.4, 0.6, 0.4
0.3, 0.3, 0.3
0.5, 0.3, –0.2
None of the above
Answer
Probability Sign. Tests - 200
If you choose a card at random from a well-shuffled
deck of 52 cards, what is the probability that the card
chosen is not a heart?
(a)
(c)
(e)
0.25
(b) 0.50
0.75
(d) 1
None of the above
Answer
Probability Sign. Tests - 300
You play tennis regularly with a friend, and from past
experience, you believe that the outcome of each match is
independent. For any given match you have a probability of
0.6 of winning. The probability that you win the next two
matches is
(a)
(c)
(e)
0.16.
0.4.
1.2.
(b) 0.36.
(d) 0.6.
Answer
Probability Sign. Tests - 400
Choose an American household at random and let X be the
number of cars (including SUVs and light trucks) they own.
Here is the probability model if we ignore the few
households that own more than 5 cars:
Number of cars X
0
1
2
3
4
5
Probability
0.09 0.36 0.35 0.13 0.05 0.02
A housing company builds houses with two-car garages.
What percent of households have more cars than the garage
can hold?
(a)
7%
(b) 13%
(c)
20%
(d) 45%
(e)
55%
Answer
Probability Sign. Tests - 500
Looking online (for example, at espn.go.com) you find the
salaries of all 22 players for the Chicago Cubs as of
opening day of the 2005 baseball season. The club total
was $87 million, eighth in the major leagues. Which
inference procedure would you use to estimate the
average salary of the Cubs players?
(a) one-sample z interval for µ
(b) one-sample t interval for µ
(c) one-sample t test
(d) one-sample z test
(e) none of these
Answer
Probability Sign. Tests - 600
You read in the report of a psychology experiment that “separate
analyses for our two groups of 12 participants revealed no overall
placebo effect for our student group (mean = 0.08, SD = 0.37, t(11) =
0.49) and a significant effect for our non-student group (mean = 0.35,
SD = 0.37, t(11) = 3.28, p < 0.01).” Are the two values given for the t
test statistic correct? (The null hypothesis is that the mean effect is zero.)
(a) Yes, both are correct.
(b) The t statistic for the student group is correct, but the one for the
non-student group is incorrect.
(c) The t statistic for the non-student group is correct, but the one for the
student group is incorrect.
(d) Both t statistics are incorrect.
(e) We can’t tell whether either t statistic is correct, because we aren’t
given the actual data.
Answer
Probability Sign. Tests - 100
Answer
A randomly selected student is asked to respond Yes, No, or
Maybe to the question “Do you intend to vote in the next
presidential election?” The sample space is { Yes, No,
Maybe }. Which of the following represents a legitimate
assignment of probabilities for this sample space?
(a)
(b)
(c)
(d)
(e)
0.4, 0.4, 0.2
0.4, 0.6, 0.4
0.3, 0.3, 0.3
0.5, 0.3, –0.2
None of the above
Probability Sign. Tests - 200
Answer
If you choose a card at random from a well-shuffled
deck of 52 cards, what is the probability that the card
chosen is not a heart?
(a)
(c)
(e)
0.25
(b) 0.50
0.75
(d) 1
None of the above
Probability Sign. Tests - 300
Answer
You play tennis regularly with a friend, and from past
experience, you believe that the outcome of each match is
independent. For any given match you have a probability of
0.6 of winning. The probability that you win the next two
matches is
(a)
(c)
(e)
0.16.
0.4.
1.2.
(b) 0.36.
(d) 0.6.
Probability Sign. Tests - 400
Answer
Choose an American household at random and let X be the
number of cars (including SUVs and light trucks) they own.
Here is the probability model if we ignore the few
households that own more than 5 cars:
Number of cars X
0
1
2
3
4
5
Probability
0.09 0.36 0.35 0.13 0.05 0.02
A housing company builds houses with two-car garages.
What percent of households have more cars than the garage
can hold?
(a)
7%
(b) 13%
(c)
20%
(d) 45%
(e)
55%
Probability Sign. Tests - 500
Answer
Looking online (for example, at espn.go.com) you find the
salaries of all 22 players for the Chicago Cubs as of
opening day of the 2005 baseball season. The club total
was $87 million, eighth in the major leagues. Which
inference procedure would you use to estimate the
average salary of the Cubs players?
(a) one-sample z interval for µ
(b) one-sample t interval for µ
(c) one-sample t test
(d) one-sample z test
(e) none of these
Probability Sign. Tests - 600
Answer
You read in the report of a psychology experiment that “separate
analyses for our two groups of 12 participants revealed no overall
placebo effect for our student group (mean = 0.08, SD = 0.37, t(11)
= 0.49) and a significant effect for our non-student group (mean =
0.35, SD = 0.37, t(11) = 3.28, p < 0.01).” Are the two values given
for the t test statistic correct? (The null hypothesis is that the mean
effect is zero.)
(a) Yes, both are correct.
(b) The t statistic for the student group is correct, but the one for the
non-student group is incorrect.
(c) The t statistic for the non-student group is correct, but the one
for the student group is incorrect.
(d) Both t statistics are incorrect.
(e) We can’t tell whether either t statistic is correct, because we aren’t
given the actual data.
Sample Tests - 100
Following a dramatic drop of 500 points in the Dow Jones
Industrial Average in September 1998, a poll conducted for
the Associated Press found that 92% of those polled said that
a year from now their family financial situation will be as
good as it is today or better. The number 92% is a
(a)
(c)
(e)
Statistic
Parameter
None of the above.
Answer
(b) Sample
(d) Population
Sample Tests - 200
In a large population, 46% of the households own VCRs. A
simple random sample of 100 households is to be contacted
and the sample proportion computed. The mean of the
sampling distribution of the sample proportion is
(a)
(b)
(c)
(d)
(e)
46
0.46
about 0.46, but not exactly 0.46
0.00248
the answer cannot be computed from the information
given.
Answer
Sample Tests - 300
If a statistic used to estimate a parameter is such that the
mean of its sampling distribution is equal to the true value of
the parameter being estimated, the statistic is said to be
(a) random
(c) a proportion
(e) none of the above.
(b) biased
(d) unbiased
Answer
Sample Tests - 400
Answer
A simple random sample of 1000 Americans found that 61% were satisfied with
the service provided by the dealer from which they bought their car. A
simple random sample of 1000 Canadians found that 58% were satisfied
with the service provided by the dealer from which they bought their car.
The sampling variability associated with these statistics is:
(a) exactly the same.
(b) smaller for the sample of Canadians because the population of Canada is
smaller than that of the United States, hence the sample is a larger
proportion of the population.
(c) smaller for the sample of Canadians because the percent satisfied was smaller
than that for the Americans.
(d) larger for the Canadians because Canadian citizens are more widely dispersed
throughout the country than in the United States, hence they have more
variable views.
(e) about the same.
Sample Tests - 500
The central limit theorem is important in statistics because it
allows us to use the Normal distribution to make inferences
concerning the population mean:
(a) provided that the sample size is reasonably large (for any
population).
(b) provided that the population is Normally distributed and the
sample size is reasonably large.
(c) provided that the population is Normally distributed (for any
sample size).
(d) provided that the population is Normally distributed and the
population variance is known (for any sample size).
(e) provided that the population size is reasonably large (whether
Answer
the population distribution is known or not).
Sample Tests - 600
Which of the following is/are correct?
I. The power of a significance test depends on the alternative value
of the parameter.
II. The probability of a Type II error is equal to the significance
level of the test.
III. Type I and Type II errors make sense only when a significance
level has been chosen in advance.
(a) I and II only
Answer
(b) I and III only
(c) II and III only
(d) I, II, and III
(e) None of the above gives the complete set of correct responses.
Sample Tests - 100 Answer
Following a dramatic drop of 500 points in the Dow Jones
Industrial Average in September 1998, a poll conducted for
the Associated Press found that 92% of those polled said that
a year from now their family financial situation will be as
good as it is today or better. The number 92% is a
(a)
(c)
(e)
Statistic
Parameter
None of the above.
(b) Sample
(d) Population
Sample Tests - 200 Answer
In a large population, 46% of the households own VCRs. A
simple random sample of 100 households is to be contacted
and the sample proportion computed. The mean of the
sampling distribution of the sample proportion is
(a)
(b)
(c)
(d)
(e)
46
0.46
about 0.46, but not exactly 0.46
0.00248
the answer cannot be computed from the information
given.
Sample Tests - 300 Answer
If a statistic used to estimate a parameter is such that the
mean of its sampling distribution is equal to the true value of
the parameter being estimated, the statistic is said to be
(a) random
(c) a proportion
(e) none of the above.
(b) biased
(d) unbiased
Sample Tests-400 Answer
A simple random sample of 1000 Americans found that 61% were satisfied with
the service provided by the dealer from which they bought their car. A
simple random sample of 1000 Canadians found that 58% were satisfied
with the service provided by the dealer from which they bought their car.
The sampling variability associated with these statistics is:
(a) exactly the same.
(b) smaller for the sample of Canadians because the population of Canada is
smaller than that of the United States, hence the sample is a larger
proportion of the population.
(c) smaller for the sample of Canadians because the percent satisfied was smaller
than that for the Americans.
(d) larger for the Canadians because Canadian citizens are more widely dispersed
throughout the country than in the United States, hence they have more
variable views.
(e) about the same.
Sample Tests - 500 Answer
The central limit theorem is important in statistics because it
allows us to use the Normal distribution to make inferences
concerning the population mean:
(a) provided that the sample size is reasonably large (for any
population).
(b) provided that the population is Normally distributed and the
sample size is reasonably large.
(c) provided that the population is Normally distributed (for any
sample size).
(d) provided that the population is Normally distributed and the
population variance is known (for any sample size).
(e) provided that the population size is reasonably large (whether
the population distribution is known or not).
Sample Tests - 600 Answer
Which of the following is/are correct?
I. The power of a significance test depends on the alternative value
of the parameter.
II. The probability of a Type II error is equal to the significance
level of the test.
III. Type I and Type II errors make sense only when a significance
level has been chosen in advance.
(a) I and II only
(b) I and III only
(c) II and III only
(d) I, II, and III
(e) None of the above gives the complete set of correct responses.
Anything Inferred - 100
A significance test allows you to reject a hypothesis in favor
of an alternative Ha at the 5% level of significance. What
can you say about significance at the 1% level?
(a) can be rejected at the 1% level of significance.
(b) There is insufficient evidence to reject at the 1% level of
significance.
(c) There is sufficient evidence to accept at the 1% level of
significance.
(d) Ha can be rejected at the 1% level of significance.
(e) The answer can’t be determined from the information
given.
Answer
Anything Inferred - 200
An analyst, using a random sample of n = 500 families, obtained a 90%
confidence interval for mean monthly family income for a large
population: ($600, $800). If the analyst had used a 99% confidence
level instead, the confidence interval would be:
(a)
(b)
(c)
(d)
(e)
Narrower and would involve a larger risk of being incorrect
Wider and would involve a smaller risk of being incorrect
Narrower and would involve a smaller risk of being incorrect
Wider and would involve a larger risk of being incorrect
Wider but it cannot be determined whether the risk of being incorrect
would be larger or smaller
Answer
Anything Inferred - 300
An opinion poll asks a random sample of adults whether they
favor banning ownership of handguns by private citizens.
A commentator believes that more than half of all adults
favor such a ban. The null and alternative hypotheses you
would use to test this claim are
(a) H0: p-hat = 0.5: Ha: p-hat > 0.5
(b) H0: p-hat = 0.5: Ha: p-hat ≠ 0.5
(c) H0: p = 0.5:
Ha: p ≠ 0.5
(d) H0: p = 0:
Ha: p > 0
(e) None of the above
Answer
Anything Inferred - 400
In preparing to use a t procedure, suppose we were not
sure if the population was Normal. In which of the
following circumstances would we not be safe using a t
procedure?
(a)
(b)
(c)
(d)
(e)
A stemplot of the data is roughly bell-shaped.
A histogram of the data shows moderate skewness.
A stemplot of the data has a large outlier.
The sample standard deviation is large.
The t procedures are robust, so it is always safe.
Answer
Anything Inferred - 500
In an opinion poll, 25% of a random sample of 200 people
said that they were strongly opposed to having a state
lottery. The standard error of the sample proportion is
approximately
(a) 0.03
(b) 0.25
(c) 0.0094
(d) 6.12
(e) 0.06
(f) None of the above.
Answer
Anything Inferred - 600
A 95% confidence interval for µ is calculated to be (1.7, 3.5).
It is now decided to test the hypothesis H0: µ = 0 versus
Ha: µ 0 at the  = 0.05 level, using the same data as
used to construct the confidence interval.
(a) We cannot test the hypothesis without the original data.
(b) We cannot test the hypothesis at the  = 0.05 level since the  = 0.05
test is connected to the 97.5% confidence interval.
(c) We can make the connection between hypothesis tests and
confidence intervals only if the sample sizes are large.
(d) We would reject H0 at level  = 0.05.
(e) We would accept H0 at level  = 0.05.
Answer
Anything Inferred - 100
Answer
A significance test allows you to reject a hypothesis in favor
of an alternative Ha at the 5% level of significance. What
can you say about significance at the 1% level?
(a) can be rejected at the 1% level of significance.
(b) There is insufficient evidence to reject at the 1% level of
significance.
(c) There is sufficient evidence to accept at the 1% level of
significance.
(d) Ha can be rejected at the 1% level of significance.
(e) The answer can’t be determined from the
information given.
Anything Inferred - 200
Answer
An analyst, using a random sample of n = 500 families, obtained a 90%
confidence interval for mean monthly family income for a large
population: ($600, $800). If the analyst had used a 99% confidence
level instead, the confidence interval would be:
(a)
(b)
(c)
(d)
(e)
Narrower and would involve a larger risk of being incorrect
Wider and would involve a smaller risk of being incorrect
Narrower and would involve a smaller risk of being incorrect
Wider and would involve a larger risk of being incorrect
Wider but it cannot be determined whether the risk of being incorrect
would be larger or smaller
Anything Inferred - 300
Answer
An opinion poll asks a random sample of adults whether they
favor banning ownership of handguns by private citizens.
A commentator believes that more than half of all adults
favor such a ban. The null and alternative hypotheses you
would use to test this claim are
(a) H0: p-hat = 0.5: Ha: p-hat > 0.5
(b) H0: p-hat = 0.5: Ha: p-hat ≠ 0.5
(c) H0: p = 0.5:
Ha: p ≠ 0.5
(d) H0: p = 0:
Ha: p > 0
(e) None of the above
Anything Inferred - 400
Answer
In preparing to use a t procedure, suppose we were not
sure if the population was Normal. In which of the
following circumstances would we not be safe using a
t procedure?
(a)
(b)
(c)
(d)
(e)
A stemplot of the data is roughly bell-shaped.
A histogram of the data shows moderate skewness.
A stemplot of the data has a large outlier.
The sample standard deviation is large.
The t procedures are robust, so it is always
safe.
Anything Inferred - 500
Answer
In an opinion poll, 25% of a random sample of 200 people
said that they were strongly opposed to having a state
lottery. The standard error of the sample proportion is
approximately
(a) 0.03
(b) 0.25
(c) 0.0094
(d) 6.12
(e) 0.06
(f) None of the above.
Anything Inferred - 600
Answer
A 95% confidence interval for µ is calculated to be (1.7, 3.5).
It is now decided to test the hypothesis H0: µ = 0 versus
Ha: µ 0 at the  = 0.05 level, using the same data as
used to construct the confidence interval.
(a) We cannot test the hypothesis without the original data.
(b) We cannot test the hypothesis at the  = 0.05 level since the  = 0.05
test is connected to the 97.5% confidence interval.
(c) We can make the connection between hypothesis tests and
confidence intervals only if the sample sizes are large.
(d) We would reject H0 at level  = 0.05.
(e) We would accept H0 at level  = 0.05.
Final Jeopardy
A scientist is weighing each of 30 fish. She obtains a mean
of 30 g and a standard deviation of 2 g. After
completing the weighing, she finds that the scale was
misaligned and always under reported every weight by 2
g that is, a fish that really weighed 26 g was reported to
weigh 24 grams. What are the mean and standard
deviation after correcting for the error in the scale?
(a) 28 g, 2 g
(c) 32 g, 2 g
(b) 30 g, 4 g
(d) 32 g, 4 g
(e) 28 g, 4 g