Stats Final Exam Questions with
Correct Answers
An entrepreneur is considering the purchase of a coin-operated laundry. The current
owner claims that over the past 5 years, the average daily revenue was $675 with a
standard deviation of $75. A sample of 30 days reveals a daily average revenue of
$625. If you were to test the null hypothesis that the daily average revenue was $675
and decide not to reject the null hypothesis, what can you conclude? - Answer-There is
not enough evidence to conclude that the daily average revenue was not $675
A manager of the credit department for an oil company would like to determine whether
the average monthly balance of credit card holders is equal to $75. An auditor selects a
random sample of 100 accounts and finds that the average owed is $83.40 with a
sample standard deviation of $23.65. If you wanted to test whether the auditor should
conclude that there is evidence that the average balance is different from $75, which
test would you use? - Answer-t-test of a population mean
A manager of the credit department for an oil company would like to determine whether
the average monthly balance of credit card holders is equal to $75. An auditor selects a
random sample of 100 accounts and finds that the average owed is $83.40 with a
sample standard deviation of $23.65. If you were to conduct a test to determine whether
the average balance is different from $75 and decided to reject the null hypothesis, what
conclusion could you draw? - Answer-There is evidence that the average balance is not
$75.
The marketing manager for an automobile manufacturer is interested in determining the
proportion of new compact-car owners who would have purchased a passenger-side
inflatable air bag if it had been available for an additional cost of $300. The manager
believes from previous information that the proportion is 0.30. Suppose that a survey of
200 new compact-car owners is selected and 79 indicate that they would have
purchased the inflatable air bags. If you were to conduct a test to determine whether
there is evidence that the proportion is different from 0.30, which test would you use? -
Answer-Z-test of a population proportion
The marketing manager for an automobile manufacturer is interested in determining the
proportion of new compact-car owners who would have purchased a passenger-side
inflatable air bag if it had been available for an additional cost of $300. The manager
believes from previous information that the proportion is 0.30. Suppose that a survey of
200 new compact-car owners is selected and 79 indicate that they would have
purchased the inflatable air bags. If you were to conduct a test to determine whether
there is evidence that the proportion is different from 0.30 and decided not to reject the
,null hypothesis, what conclusion could you draw? - Answer-There is not sufficient
evidence that the proportion is not 0.30
Microsoft Excel was used on a set of data involving the number of parasites found on 46
Monarch butterflies captured in Pismo Beach State Park. A biologist wants to know if
the mean number of parasites per butterfly is over 20. She will make her decision using
a test with a level of significance of 0.10. The following information was extracted from
the Microsoft Excel output for the sample of 46 Monarch butterflies: n = 46; Arithmetic
Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82; Null Hypothesis: H0 :
<=20.000; a = 0.10; df = 45; T Test Statistic = 2.09; One-Tailed Test Upper Critical
Value = 1.3006; p-value = 0.021; Decision = Reject
Referring to Table 9-1, the parameter the biologist is interested in is: - Answer-the mean
number of parasites on Monarch butterflies in Pismo Beach State Park
Referring to Table 9-1, state the alternative hypothesis for this study. - Answer-H1: >
20.000
Referring to Table 9-1, what critical value should the biologist use to determine the
rejection region? - Answer-1.3006
A spouse suspects that the average amount of money spent on Christmas gifts for
immediate family members is above $1,200. The correct set of hypotheses is: - Answer-
H0: μ = 1200 vs. H1: μ > 1200
In testing the hypothesis H0: μ = 100 vs. H1: μ > 100, the p-value is found to be 0.074,
and the sample mean is 105. Which of the following statements is true? - Answer-The
probability of observing a sample mean at least as large as 105 from a population
whose mean is 100 is 0.074
A random sample of 8 observations was drawn from a normal population. The sample
mean and population standard deviation are 40 and 10 respectively. Estimate the
population mean with 95% confidence (to 2 decimals) - Answer-(33.07, 46.93)
A random sample of 8 observations was drawn from a normal population. The sample
mean and sample standard deviation are 40 and 10 respectively. Estimate the
population mean with 95% confidence (to 2 decimals). - Answer-(31.64, 48.36)
The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with μ =
110 grams and σ = 25 grams. What is the probability that a randomly selected vitamin
will contain between 100 and 110 grams of pyridoxine? - Answer-0.1554
When determining the sample size for a proportion for a given level of confidence and
sampling error, the closer to 0.50 that π is estimated to be, the sample size required
________. - Answer-larger
, The width of a confidence interval estimate for a proportion will be - Answer-narrower
for 90% confidence than for 95% confidence.
A 99% confidence interval estimate can be interpreted to mean that - Answer-both of
the above
If you were constructing a 99% confidence interval of the population mean based on a
sample of n = 25, where the standard deviation of the sample s = 0.05, the critical value
of t will be - Answer-2.7970.
Which of the following is NOT true about the Student's t distribution? - Answer-It is used
to construct confidence intervals for the population mean when the population standard
deviation is known.
Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). Give a definition
of what it means to be "95% confident" as an inference. - Answer-In repeated sampling,
95% of the intervals constructed would contain the population mean.
Suppose a 95% confidence interval for has been constructed. If it is decided to take a
larger sample and to decrease the confidence level of the interval, then the resulting
interval width would . (Assume that the sample statistics gathered would not change
very much for the new sample.) - Answer-be narrower than the current interval width
In the construction of confidence intervals, if all other quantities are unchanged, an
increase in the sample size will lead to an interval that's.. - Answer-narrower
A major department store chain is interested in estimating the average amount its credit
card customers spent on their first visit to the chain's new store in the mall. Fifteen credit
card accounts were randomly sampled and analyzed with the following results: X =
$50.50 and s 2 = 400 . Assuming the distribution of the amount spent on their first visit
is approximately normal, what is the shape of the sampling distribution of the sample
mean that will be used to create the desired confidence interval for - Answer-A t
distribution with 14 degrees of freedom
A major department store chain is interested in estimating the average amount its credit
card customers spent on their first visit to the chain's new store in the mall. Fifteen credit
card accounts were randomly sampled and analyzed with the following results: $50.50
X = and s 2 = 400 . Construct a 95% confidence interval for the average amount its
credit card customers spent on their first visit to the chain's new store in the mall
assuming that the amount spent follows a normal distribution - Answer-$50.50 +- $11.08
Private colleges and universities rely on money contributed by individuals and
corporations for their operating expenses. Much of this money is put into a fund called
an endowment, and the college spends only the interest earned by the fund. A recent
survey of 8 private colleges in the United States revealed the following endowments (in
millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. What value
Correct Answers
An entrepreneur is considering the purchase of a coin-operated laundry. The current
owner claims that over the past 5 years, the average daily revenue was $675 with a
standard deviation of $75. A sample of 30 days reveals a daily average revenue of
$625. If you were to test the null hypothesis that the daily average revenue was $675
and decide not to reject the null hypothesis, what can you conclude? - Answer-There is
not enough evidence to conclude that the daily average revenue was not $675
A manager of the credit department for an oil company would like to determine whether
the average monthly balance of credit card holders is equal to $75. An auditor selects a
random sample of 100 accounts and finds that the average owed is $83.40 with a
sample standard deviation of $23.65. If you wanted to test whether the auditor should
conclude that there is evidence that the average balance is different from $75, which
test would you use? - Answer-t-test of a population mean
A manager of the credit department for an oil company would like to determine whether
the average monthly balance of credit card holders is equal to $75. An auditor selects a
random sample of 100 accounts and finds that the average owed is $83.40 with a
sample standard deviation of $23.65. If you were to conduct a test to determine whether
the average balance is different from $75 and decided to reject the null hypothesis, what
conclusion could you draw? - Answer-There is evidence that the average balance is not
$75.
The marketing manager for an automobile manufacturer is interested in determining the
proportion of new compact-car owners who would have purchased a passenger-side
inflatable air bag if it had been available for an additional cost of $300. The manager
believes from previous information that the proportion is 0.30. Suppose that a survey of
200 new compact-car owners is selected and 79 indicate that they would have
purchased the inflatable air bags. If you were to conduct a test to determine whether
there is evidence that the proportion is different from 0.30, which test would you use? -
Answer-Z-test of a population proportion
The marketing manager for an automobile manufacturer is interested in determining the
proportion of new compact-car owners who would have purchased a passenger-side
inflatable air bag if it had been available for an additional cost of $300. The manager
believes from previous information that the proportion is 0.30. Suppose that a survey of
200 new compact-car owners is selected and 79 indicate that they would have
purchased the inflatable air bags. If you were to conduct a test to determine whether
there is evidence that the proportion is different from 0.30 and decided not to reject the
,null hypothesis, what conclusion could you draw? - Answer-There is not sufficient
evidence that the proportion is not 0.30
Microsoft Excel was used on a set of data involving the number of parasites found on 46
Monarch butterflies captured in Pismo Beach State Park. A biologist wants to know if
the mean number of parasites per butterfly is over 20. She will make her decision using
a test with a level of significance of 0.10. The following information was extracted from
the Microsoft Excel output for the sample of 46 Monarch butterflies: n = 46; Arithmetic
Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82; Null Hypothesis: H0 :
<=20.000; a = 0.10; df = 45; T Test Statistic = 2.09; One-Tailed Test Upper Critical
Value = 1.3006; p-value = 0.021; Decision = Reject
Referring to Table 9-1, the parameter the biologist is interested in is: - Answer-the mean
number of parasites on Monarch butterflies in Pismo Beach State Park
Referring to Table 9-1, state the alternative hypothesis for this study. - Answer-H1: >
20.000
Referring to Table 9-1, what critical value should the biologist use to determine the
rejection region? - Answer-1.3006
A spouse suspects that the average amount of money spent on Christmas gifts for
immediate family members is above $1,200. The correct set of hypotheses is: - Answer-
H0: μ = 1200 vs. H1: μ > 1200
In testing the hypothesis H0: μ = 100 vs. H1: μ > 100, the p-value is found to be 0.074,
and the sample mean is 105. Which of the following statements is true? - Answer-The
probability of observing a sample mean at least as large as 105 from a population
whose mean is 100 is 0.074
A random sample of 8 observations was drawn from a normal population. The sample
mean and population standard deviation are 40 and 10 respectively. Estimate the
population mean with 95% confidence (to 2 decimals) - Answer-(33.07, 46.93)
A random sample of 8 observations was drawn from a normal population. The sample
mean and sample standard deviation are 40 and 10 respectively. Estimate the
population mean with 95% confidence (to 2 decimals). - Answer-(31.64, 48.36)
The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with μ =
110 grams and σ = 25 grams. What is the probability that a randomly selected vitamin
will contain between 100 and 110 grams of pyridoxine? - Answer-0.1554
When determining the sample size for a proportion for a given level of confidence and
sampling error, the closer to 0.50 that π is estimated to be, the sample size required
________. - Answer-larger
, The width of a confidence interval estimate for a proportion will be - Answer-narrower
for 90% confidence than for 95% confidence.
A 99% confidence interval estimate can be interpreted to mean that - Answer-both of
the above
If you were constructing a 99% confidence interval of the population mean based on a
sample of n = 25, where the standard deviation of the sample s = 0.05, the critical value
of t will be - Answer-2.7970.
Which of the following is NOT true about the Student's t distribution? - Answer-It is used
to construct confidence intervals for the population mean when the population standard
deviation is known.
Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). Give a definition
of what it means to be "95% confident" as an inference. - Answer-In repeated sampling,
95% of the intervals constructed would contain the population mean.
Suppose a 95% confidence interval for has been constructed. If it is decided to take a
larger sample and to decrease the confidence level of the interval, then the resulting
interval width would . (Assume that the sample statistics gathered would not change
very much for the new sample.) - Answer-be narrower than the current interval width
In the construction of confidence intervals, if all other quantities are unchanged, an
increase in the sample size will lead to an interval that's.. - Answer-narrower
A major department store chain is interested in estimating the average amount its credit
card customers spent on their first visit to the chain's new store in the mall. Fifteen credit
card accounts were randomly sampled and analyzed with the following results: X =
$50.50 and s 2 = 400 . Assuming the distribution of the amount spent on their first visit
is approximately normal, what is the shape of the sampling distribution of the sample
mean that will be used to create the desired confidence interval for - Answer-A t
distribution with 14 degrees of freedom
A major department store chain is interested in estimating the average amount its credit
card customers spent on their first visit to the chain's new store in the mall. Fifteen credit
card accounts were randomly sampled and analyzed with the following results: $50.50
X = and s 2 = 400 . Construct a 95% confidence interval for the average amount its
credit card customers spent on their first visit to the chain's new store in the mall
assuming that the amount spent follows a normal distribution - Answer-$50.50 +- $11.08
Private colleges and universities rely on money contributed by individuals and
corporations for their operating expenses. Much of this money is put into a fund called
an endowment, and the college spends only the interest earned by the fund. A recent
survey of 8 private colleges in the United States revealed the following endowments (in
millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. What value
