1
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:
a.) 2.7969.
b.) 2.7874.
c.) 2.4922.
d.) 2.4851.
2
The diameter of Ping-Pong balls manufactured at a large factory is expected to be approximately
normally distributed with a mean of 1.30 inches and a standard deviation of 0.04 inch. What is the
probability that a randomly selected Ping-Pong ball will have a diameter between 1.31 and 1.33
inches?
a.) 0.0987
b.) 0.1747
c.) 0.2734
d.) 0.3721
3
The width of a confidence interval estimate for a proportion will be:
a.) narrower for 99% confidence than for 95% confidence.
b.) wider for a sample size of 100 than for a sample size of 50.
c.) narrower for 90% confidence than for 95% confidence,
d.) narrower when the sample proportion is 0.50 than when the sample proportion is 0.20.
4
Assume that house prices in a neighborhood are normally distributed with standard deviation
$20,000. A random sample of 16 observations is taken. What is the probability that the sample
mean differs from the population mean by more than $5,000?
a.) 0.3174
b.) 0.1587
c.) 0, because it is assumed that the sample mean is equal to the population mean in a normally
distributed population.
d.) Cannot be determined from the information given.
5
The standard error of the mean:
a.) is never larger than the standard deviation of the population,
b.) decreases as the sample size increases.
c.) measures the variability of the mean from sample to sample.
d.) all of the above.
6
Which of the following is true about the sampling distribution of the sample mean?
a.) The mean of the sampling distribution is always μ.
b.) The standard deviation of the sampling distribution is always s.
c.) The shape of the sampling distribution is always approximately normal.
d.) All of the above are true.
7
For air travelers, one of the biggest complaints is of the waiting time between when the airplane
taxis away from the terminal until the flight takes off. This waiting time is known to have a
skewed-right distribution with a mean of 10 minutes and a standard deviation of 8 minutes.
Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean
waiting time between when the airplane taxis away from the terminal until the flight takes off for
these 100 flights.
a.) Distribution is skewed-right with mean = 10 minutes and standard error = 0.8 minutes.
b.) Distribution is skewed-right with mean = 10 minutes and standard error = 8 minutes.
c.) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8
minutes.
d.) Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes.
8
An economist is interested in studying the incomes of consumers in a particular region. The
population standard deviation is known to be $1,000. A random sample of 50 individuals resulted
in an average income of $15,000. What is the upper end point in a 99% confidence interval for the
average income?
a.) $15,052
b.) $15,141
c.) $15,330
d.) $15,364
9
When determining the sample size necessary for estimating the true population mean, which
factor is not considered when sampling with replacement?
a.) The population size
b.) The population standard deviation
c.) The level of confidence desired in the estimate
d.) The allowable or tolerable sampling error
10
A confidence interval was used to estimate the proportion of statistics students that are female. A
random sample of 72 statistics students generated the following 90% confidence interval: (0.438,
0.642). Using the information above, what size sample would be necessary if we wanted to
estimate the true proportion to within ±0.08 using 95% confidence?
a.) 105
b.) 150
c.) 420
d.) 597
11
The standard error of the mean for a sample of 100 is 30. In order to manipulate the standard error
of the mean to be 15, we would:
a.) increase the sample size to 200.
b.) increase the sample size to 400.
c.) decrease the sample size to 50.
d.) decrease the sample size to 25.
12
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 : L J = $50. 50 s2 and = 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 μ0
a.) Approximately normal with a mean of $50.50
b.) A standard normal distribution
c.) A t distribution with 15 degrees of freedom
d.) A t distribution with 14 degrees of freedom
13
When determining the sample size for a proportion for a given level of confidence and sampling
error, the closer to 0.50 that p is estimated to be, the the sample size required.
a.) smaller
b.) larger
c.) sample size is not affected
d.) the effect cannot be determined from the information given
14
A statistician wishes to estimate the average total compensation of CEOs in the service industry.
Data were randomly collected from 18 CEOs and the 97% confidence interval was calculated to
be ($2,181 ,260, $5,836, 180). Which of the following interpretations is correct?
a.) 97% of the sampled total compensation values fell between $2,181,260 and $5,836,180.
b.) We are 97% confident that the mean of the sampled CEOs falls in the interval $2,181,260 to
$5,836,180.
c.) In the population of service industry CEOs, 97% of them will have total compensations that
fall in the interval $2,181,260 to $5,836,180.
d.) We are 97% confident that the average total compensation of all CEOs in the service industry
falls in the interval $2,181,260 to $5,836,180.
15
The use of the finite population correction factor when sampling without replacement from finite
populations will:
a.) increase the standard error of the mean.
b.) not affect the standard error of the mean.
c.) reduce the standard error of the mean.
d.) only affect the proportion, not the mean.
16
An internal control policy for an online fashion accessories store requires a quality assurance
check before a shipment is made. The tolerable exception rate for this internal control is 0.05.
During an audit, 500 shipping records were sampled from a population of 5,000 shipping records
and 12 were found that violated the control. What is the upper bound for a 95% one-sided
confidence interval estimate for the rate of noncompliance?
a.) 0.0060
b.) 0.0067
c.) 0.0347
d.) 0.0374
17
A stationery store wants to estimate the total retail value of the 300 greeting cards that it has in its
inventory. What are the upper and lower limits of the 95% confidence interval estimate of the
population total value of all greeting cards that are in inventory if a random sample of 20 greeting
cards indicates an average value of $1.67 and a standard deviation of $0.32?
a.) $457.52 and $544.48
b.) $465.08 and $536.92
c.) $460.29 and $541.72
d.) $457.67 and $544.33
18
Which of the following is not true about the student's t distribution?
a.) It has more area in the tails and less in the center than does the normal distribution.
b.) It is used to construct confidence intervals for the population mean when the population
standard deviation is known.
c.) It is bell-shaped and symmetrical.
d.) As the number of degrees of freedom increases, the t distribution approaches the normal
distribution.
19
If the expectation of a sampling distribution is located at the parameter it is estimating, then we
call that sampling distribution:
a.) unbiased.
b.) minimum variance.
c.) biased.
d.) random.
20
The personnel director of a large corporation wishes to study absenteeism among clerical workers
at the corporation's central office during the year. A random sample of 25 clerical workers
revealed the following:
Absenteeism : U = 9.7 days and S = 4.0 days
12 clerical workers were absent more than 10 days
What are the upper and lower limits of the 95% confidence interval estimate of the mean number
of absences for clerical workers last year
a.) 8.132 and 11.268
b.) 8.049 and 11.351
c.) 8.052 and 11.348
d.) 8.331 and 11.069
21
Why is the Central Limit Theorem so important to the study of sampling distributions?
a.) It allows us to disregard the size of the sample selected when the population is not normal.
b.) It allows us to disregard the shape of the sampling distribution when the size of the population
is large.
c.) It allows us to disregard the size of the population we are sampling from.
d.) It allows us to disregard the shape of the population when n is large.
22
Approximately 5% of U.S. families have a net worth in excess of $1 million and thus can be
called "millionaires." However, a survey in the year 2000 found that 30% of Microsoft's 31,000
employees were millionaires. If random samples of 100 Microsoft employees had been taken that
year, what proportion of the samples would have been between 25% and 35% millionaires?
a.) 0.1379
b.) 0.2758
c.) 0.7242
d.) 1.0911
23
A 99% confidence interval estimate can be interpreted to mean that:
a.) if all possible samples are taken and confidence interval estimates are developed, 99% of them
would include the true population mean somewhere within their interval.
b.) we have 99% confidence that we have selected a sample whose interval does include the
population mean.
c.) both of the above.
d.) none of the above.
24
The fill amount of bottles of soft drink has been found to be normally distributed with a mean of
2.0 liters and a standard deviation of 0.05 liter. If a random sample of bottles is selected, what is
the probability that the sample mean will be between 1.99 and 2.0 liters?
a.) 0.4772
b.) 0.5228
c.) 0.9544
d.) Cannot be determined from the information given.
25
For sample size 16, the sampling distribution of the mean will be approximately normally
distributed:
a.) regardless of the shape of the population.
b.) if the shape of the population is symmetrical.
c.) if the sample standard deviation is known.
d.) if the sample is normally distributed.