FRAPPY Test AP Stats Questions With Complete Solutions
A humane society wanted to estimate with 95% confidence the
prop. of households in its county that own at least one dog.
A) Interpret the 95% confidence level in this context. Correct
Answers The 95% confidence level means that if one were to
repeatedly take random samples of the same size from the
population and construct a 95% confidence interval from each
sample, then in the long run 95% of the those intervals would
capture the actual value of the pop. prop. of the households w/
@ least 1 dog.
A humane society wanted to estimate with 95% confidence the
prop. of households in its county that own at least one dog. The
humane society selected a random sample of households in its
country and used the sample to estimate the prop. of all
households that own at least one dog. The conditions for
calculating a 95% confidence interval for the prop. of
households in this county that own at least one dog were
checked and verified and the resulting confidence interval
was .417 (+/-) .119
B) A national pet products association claimed that 39% of all
America households owned at least one dog. Does the humane
society's interval estimate provide evidence that the proportion
of dog owners in its country is different from the claimed
national proportion? Explain. Correct Answers No. The 95%
confidence interval is the interval (.298, .536). This interval
includes .39 as a plausible value for the population proportion of
households in the country that own at least one dog. Therefore,
the confidence interval does not provide evidence that the
,proportion of dog owners in this county is different from the
population.
A humane society wanted to estimate with 95% confidence the
prop. of households in its county that own at least one dog. The
humane society selected a random sample of households in its
country and used the sample to estimate the prop. of all
households that own at least one dog. The conditions for
calculating a 95% confidence interval for the prop. of
households in this county that own at least one dog were
checked and verified and the resulting confidence interval
was .417 (+/-) .119
C) How many households were selected in the humane society's
sample? Show how you obtained your answer. Correct Answers
.119= sqroot((.417*(1-.417))/n)
n= 65.95
A simple random sample of adults living in a suburb of a large
city was selected. The age and annual income of each adult in
the sample were recorded. The resulting data are summarized in
the table below.
A) What is the probability that a person chosen at random from
those in this sample will be in the 31-45 age category? Correct
Answers P(age 31-45)= 89/207 = .42995
A simple random sample of adults living in a suburb of a large
city was selected. The age and annual income of each adult in
the sample were recorded. The resulting data are summarized in
the table below.
B) What is the probability that a person chosen at random from
those in this sample whose incomes are over $50,000 will be in
, the 31-45 category? Show your work Correct Answers P(age
31-45 I income over 50000)= 35/96 = .36458
A simple random sample of adults living in a suburb of a large
city was selected. The age and annual income of each adult in
the sample were recorded. The resulting data are summarized in
the table below.
C) Based on your answers to parts (a) and (b), is annual income
independent of age category for those in this sample. Explain.
Correct Answers If annual income and age were independent,
the probabilities in a and b would be equal and since they're not
equal, they are not independent.
An administrator at a large university wants to conduct a survey
to estimate the proportion of students who are satisfied with the
appearance of the university buildings and grounds. The
administrator is considering three methods of obtaining a sample
of 500 students from the 70,000 students at the university.
A) Because of financial constraints, the first method the
administrator is considering consists of taking a convenience
sample ton keep the expenses low. A very large number of
students will attend the first football game of the season, and the
first 500 students who enter the football stadium could be used
as a sample. Why might such a sampling method be biased in
producing an estimate of the proportion of students who are
satisfied with the appearance of the buildings and grounds?
Correct Answers The first 500 students do not represent the
whole population of the school. It is likely that most of those
students that attended the football game have school pride,
which could be related to their opinion about how the school
looks.
A humane society wanted to estimate with 95% confidence the
prop. of households in its county that own at least one dog.
A) Interpret the 95% confidence level in this context. Correct
Answers The 95% confidence level means that if one were to
repeatedly take random samples of the same size from the
population and construct a 95% confidence interval from each
sample, then in the long run 95% of the those intervals would
capture the actual value of the pop. prop. of the households w/
@ least 1 dog.
A humane society wanted to estimate with 95% confidence the
prop. of households in its county that own at least one dog. The
humane society selected a random sample of households in its
country and used the sample to estimate the prop. of all
households that own at least one dog. The conditions for
calculating a 95% confidence interval for the prop. of
households in this county that own at least one dog were
checked and verified and the resulting confidence interval
was .417 (+/-) .119
B) A national pet products association claimed that 39% of all
America households owned at least one dog. Does the humane
society's interval estimate provide evidence that the proportion
of dog owners in its country is different from the claimed
national proportion? Explain. Correct Answers No. The 95%
confidence interval is the interval (.298, .536). This interval
includes .39 as a plausible value for the population proportion of
households in the country that own at least one dog. Therefore,
the confidence interval does not provide evidence that the
,proportion of dog owners in this county is different from the
population.
A humane society wanted to estimate with 95% confidence the
prop. of households in its county that own at least one dog. The
humane society selected a random sample of households in its
country and used the sample to estimate the prop. of all
households that own at least one dog. The conditions for
calculating a 95% confidence interval for the prop. of
households in this county that own at least one dog were
checked and verified and the resulting confidence interval
was .417 (+/-) .119
C) How many households were selected in the humane society's
sample? Show how you obtained your answer. Correct Answers
.119= sqroot((.417*(1-.417))/n)
n= 65.95
A simple random sample of adults living in a suburb of a large
city was selected. The age and annual income of each adult in
the sample were recorded. The resulting data are summarized in
the table below.
A) What is the probability that a person chosen at random from
those in this sample will be in the 31-45 age category? Correct
Answers P(age 31-45)= 89/207 = .42995
A simple random sample of adults living in a suburb of a large
city was selected. The age and annual income of each adult in
the sample were recorded. The resulting data are summarized in
the table below.
B) What is the probability that a person chosen at random from
those in this sample whose incomes are over $50,000 will be in
, the 31-45 category? Show your work Correct Answers P(age
31-45 I income over 50000)= 35/96 = .36458
A simple random sample of adults living in a suburb of a large
city was selected. The age and annual income of each adult in
the sample were recorded. The resulting data are summarized in
the table below.
C) Based on your answers to parts (a) and (b), is annual income
independent of age category for those in this sample. Explain.
Correct Answers If annual income and age were independent,
the probabilities in a and b would be equal and since they're not
equal, they are not independent.
An administrator at a large university wants to conduct a survey
to estimate the proportion of students who are satisfied with the
appearance of the university buildings and grounds. The
administrator is considering three methods of obtaining a sample
of 500 students from the 70,000 students at the university.
A) Because of financial constraints, the first method the
administrator is considering consists of taking a convenience
sample ton keep the expenses low. A very large number of
students will attend the first football game of the season, and the
first 500 students who enter the football stadium could be used
as a sample. Why might such a sampling method be biased in
producing an estimate of the proportion of students who are
satisfied with the appearance of the buildings and grounds?
Correct Answers The first 500 students do not represent the
whole population of the school. It is likely that most of those
students that attended the football game have school pride,
which could be related to their opinion about how the school
looks.
