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Employees of a local university have been classified according to gender and job type.
If an employee is selected at random, what is the probability that the employee is a
member of the hourly staff, given that the employee is female?
A. 0.400
B. 0.133
C. 0.160
D. 0.053
E. 0.533
A manufacturing company produces part QV2Y for the aerospace industry. This
particular part can be manufactured using 3 different production processes. The
management wants to know if the quality of the units of part QV2Y is the same for all
three processes. The production supervisor obtained the following data: Process 1 had
29 defective units in 240 items, Process 2 produced 12 defective units in 180 items, and
Process 3 manufactured 9 defective units in 150 items.
Chi-Square Contingency Table Test for Independence
At a significance level of .05, the management wants to perform a hypothesis test to
determine if the quality of the items produced appears to be independent of the
production process used. Based on the results summarized in the MegaStat/Excel output
provided in the table above, we
A. reject H0 and conclude that the quality of the product is not the same for all
processes.
B. reject H0 and conclude that the quality of the product is dependent on the
manufacturing process.
C. do not reject H0, and conclude that the quality of the product does not significantly
differ among the three processes.
D. do not reject H0, and conclude that the quality of the product is not the same for all
processes.
E. reject H0 and conclude that the quality of the product is independent of the
manufacturing process used.
If = 2.0144, = .0972, and there are 25 subgroups of size 5, find the UCL and the
LCL for the R chart.
A. [.045, .1498]
B. [.0972, .2055]
C. [0, .2055]
D. [0.2, 114]
The weight of a product is normally distributed with a mean of four ounces and a
variance of .25 squared ounces. The company wants to classify the unit as a scrap in a
maximum of 1 percent of the units if the weight is below a desired value. Determine the
desired weight such that no more than 1 percent of the units are below it.
A. 3.360
B. 3.680
C. 2.835
D. 3.418
Refer to the MegaStat/Excel output for the Wilcoxon signed ranks test given in the table
below.
At a significance level of .01, which one of the following rejection point conditions is
correct regarding the null hypothesis, H0: D1 and D2 are identical probability
distributions, and the alternative hypothesis of Ha: D1 is shifted to the left of D2.
A. We reject H0 and conclude there is not sufficient evidence that the probability
distribution of population 1 is shifted to the left of the probability distribution of
population 2.
B. We cannot reject H0 and conclude there is not sufficient evidence that the probability
distribution of population 1 is shifted to the left of the probability distribution of
population 2.
C. We reject H0 and conclude there is very strong evidence that the probability
distribution of population 1 is shifted to the left of the probability distribution of
population 2.
D. We do not reject H0 and conclude there is very strong evidence that the probability
distribution of population 1 is shifted to the left or to the right of the probability
distribution of population 2.
E. We do not reject H0 and conclude there is very strong evidence that the probability
distribution of population 1 is identical to the probability distribution of population 2.
A sample of 2,000 people yielded =.52. Calculate a 90 percent confidence interval for
p.
A. [.506, .534]
B. [.468, .572]
C. [.511, .529]
D. [.502, .538]
A pair of dice is thrown. What is the probability that one of the faces is a 3, given that
the sum of the two faces is 9?
A. 1/3
B. 1/36
C. 1/6
D. 1/2
E. 1/4
The following is a relative frequency distribution of grades in an introductory statistics
course.
If this was the distribution of 200 students, find the frequency of failures.
A. 12
B. 6
C. 23
D. 46
E. 3
The ___________ component of a time series reflects the long-run decline or growth in
a time series.
A. trend
B. seasonal
C. cyclical
D. irregular
The width of a confidence interval will be
A. narrower for 99 percent confidence than for 95 percent confidence.
B. wider for a sample size of 100 than for a sample size of 50.
C. narrower for 90 percent confidence than for 95 percent confidence.
D. wider when the sample standard deviation (s) is small than when s is large.
When using a multiple regression model, we assume that error terms (residuals) are
distributed according to a(n) ________________ distribution.
A. binomial
B. normal
C. exponential
D. Poisson
A study was conducted to investigate the effect of coaching on IQ tests. Nine randomly
selected students were tested.
Before After
100 106
111 112
93 95
92 90
99 107
85 100
117 126
110 105
98 110
Calculate T− and T+.
A. 44, 1
B. 38.5, 6.5
C. 45.5, 2.5
D. 32.5, 12.5
For a given hypothesis test, if we do not reject H0, and H0 is true,
A. no error has been committed.
B. a Type I error has been committed.
C. a Type II error has been committed.
D. a Type III error has been committed.
A random sample of size 1,000 is taken from a population where p = .20. Find P( > .
175).
A. .9761
B. .0239
C. .0392
D. .9999
In general, a multiple regression model is considered to be desirable if the value of the
C statistic is small and the value of C is less than _____.
A. k
B. k − 1
C. k + 1
D. n − k
According to Chebyshev's Theorem, at least what proportion of the data will be within
μ kσ for k = 2?
A. 68%
B. 50%
C. 25%
D. 75%
E. 34%
A cable TV company wants to estimate the percentage of cable boxes in use during an
evening hour. An approximation is 20 percent. They want the estimate to be at the 90
percent confidence level and within 2 percent of the actual proportion. What sample
size is needed?
A. 22
B. 1692
C. 1537
D. 1083
The number of weekly sales calls by a sample of 25 pharmaceutical salespersons is
below.
24, 56, 43, 35, 37, 27, 29, 44, 34, 28, 33, 28, 46, 31, 38, 41, 48, 38, 27, 29, 37, 33, 31,
40, 50
How many classes should be used in the construction of a histogram?
A. 4
B. 6
C. 10
D. 5
E. 2
The point estimate of the variance in a regression model is
A. SSE.
B. b0.
C. MSE.
D. b1.
Which one of the following is not an assumption of one-way analysis of variance?
A. random selection of samples from each population
B. equality of the population variances
C. equality of the population means
D. Samples selected from each treatment population all have normal distributions.
Consider a Poisson distribution with an average of 3 customers per minute at the local
grocery store. If X = the number of arrivals per minute, find the expected value of X.
A. 3
B. 9
C. 1.5
D. 1.7
Use this information about 10 shipments of lightbulbs.
Shipment 1 2 3 4 5 6 7 8 9 10
# of defective units 0 1 2 0 4 3 2 1 3 4
If 200 lightbulbs are selected at random from each of 10 shipments and the number of
defectives in each shipment is given above, find the LCL and the UCL for the p chart.
A. [0, .1044]
B. [.003, .017]
C. [0, .0311]
D. [.009, .0115]
Suppose that the waiting time for a license plate renewal at a local office of a state
motor vehicle department has been found to be normally distributed with a mean of 30
minutes and a standard deviation of 8 minutes. What is the probability that a randomly
selected individual will have a waiting time of at least 10 minutes?
A. .9938
B. .8944
C. .1056
D. .0062
A powder metal manufacturing company is producing sleeves for a locking mechanism.
The target (nominal) value for the inside diameter is 1 inch. The inside diameter
specifications are 1 .005 inches. Assume that the process is in statistical control with =
1.0002 inches, = .003 inches, and subgroup size of 5. What are the natural tolerance
limits for this process? Is the process capable?
A. .99847 to 1.00193, yes
B. .99847 to 1.00193, no
C. .99633 to 1.004, yes
D. .99633 to 1.004, no
E. .995 to 1.005, yes
A company collected the ages from a random sample of its middle managers, with the
resulting frequency distribution shown below.
What is the midpoint of the third class interval?
A. 22.5
B. 27.5
C. 32.5
D. 37.5
E. 42.5
A(n) ____________ process has the ability to produce products or services that meet
customer requirements.
A. in-control
B. assignable
C. capable
D. statistical
It is appropriate to use the uniform distribution to describe a continuous random
variable x when
A. the area under the probability curve = 1.
B. the probability curve f(x) > 0.
C. the shape of the histogram of all possible values of x is nonsymmetrical.
D. relative frequencies of all possible values of x are about the same.
Consider the following data.
Calculate S5 using simple exponential smoothing if S3 = 19.064 and α = 0.2.
Consider the experiment of tossing a fair coin three times and observing the number of
heads that result (X = number of heads). What is the variance for this distribution?
A. 1.5
B. 1.22
C. 0.75
D. 0.87
The measurement in a sample or a population that occurs most frequently is the
___________.
A. mode
B. mean
C. median
D. outlier
E. average
If events A and B are independent, then the probability of simultaneous occurrence of
event A and event B can be found with ____________.
A. P(A)P(B)
B. P(A)P(B|A)
C. P(B)P(A|B)
D. All of these choices are correct.
A manufacturer of windows produces one type that has a plastic coating. The
specification limits for the plastic coating are 30 and 70. From time to time the plastic
coating can become uneven. Therefore, to keep the coating as even as possible,
thickness measurements are periodically taken at four different locations on the
window. 15 subgroups were observed, each consisting of four thickness measurements,
with the following results: mean of the means = = 50.05, and average range of 8.85.
Assuming that the process is in statistical control, calculate the natural tolerance limits
for the process.
A. [45.75, 54.35]
B. [37.16, 62.94]
C. [42.40, 57.70]
D. [47.50, 52.60]
In an opinion survey, a random sample of 1,000 adults from the United States and 1,000
adults from Germany were asked whether they supported the death penalty. 590
American adults and 560 German adults indicated that they supported the death penalty.
The researcher wants to know whether there is sufficient evidence to conclude that the
proportion of adults who support the death penalty is higher in the United States than in
Germany. What is the decision at α = .05?
The manager of a grocery store wants to determine whether the amount of water
contained in 1-gallon bottles purchased from a nationally known manufacturer actually
averages 1 gallon. It is known from the specifications that the standard deviation of the
amount of water is equal to 0.02 gallon. A random sample of 32 bottles is selected, and
the mean amount of water per 1-gallon bottle is found to be 0.995 gallon. Calculate the
p-value and test whether the specifications are being met at α = .001 using the p-value
rule.
Consider the 3 x 2 contingency table below.
At a significance level of .05, test H0: the factors A and B are independent.
What is the degrees of freedom error (within-group variation) of a completely
randomized design (one-way) ANOVA test with 4 groups and 15 observations per each
group?
A company that fills one-gallon containers of water has four machines. The quality
control manager needs to determine whether the average fill for these machines is the
same. For a sample of 19 one-gallon containers, we have the following data of fill
measures (x) in quarts.
Machine 1 Machine 2 Machine 3 Machine 4
N 4 6 5 4
4.03 4.0017 3.974 4.005
S 0.0183 0.0117 0.0182 0.0129
And the following partial ANOVA table.
Source SS DF MS F
Treatment 0.002359
Error
Total 0.010579
Determine the degrees of freedom for the treatment, error, and total, and state the
critical value of the F statistic at α = .05.
When we test H0: p1 − p2 .01, HA: p1 − p2> .01, at α = .05, where 1 = .08, 2 = .035,
n1 = 200, and n2 = 400, what is the standard deviation used to calculate the test
statistic?
Use the following price information for three grains.
Calculate the Paasche index.
A local tire dealer wants to predict the number of tires sold each month. He believes
that the number of tires sold is a linear function of the amount of money invested in
advertising. He randomly selects 6 months of data consisting of tire sales (in thousands
of tires) and advertising expenditures (in thousands of dollars). Based on the data set
with 6 observations, the simple linear regression model yielded the following results.
Determine the values of SSE and SST.
A major car manufacturer wants to test a new catalytic converter to determine whether
it meets new air pollution standards. The mean emission of all converters of this type
must be less than 20 parts per million of carbon monoxide. Ten (10) converters are
manufactured for testing purposes and their emission levels are measured, with a mean
of 17.17 and a standard deviation of 2.98. Calculate the appropriate test statistic to test
the hypotheses using the critical value rule.
Consider the following partial analysis of variance table from a randomized block
design with 10 blocks and 6 treatments.
Source SS
Treatments 2,477.53
Blocks 3,180.48
Error 11,661.38
Total
Determine the degrees of freedom for the blocks.
Consider the following one-way ANOVA table.
Source df Sum of Squares
Model 3 213.88125
Error 20 11.208333
Total 23 225.0895
If there are an equal number of observations in each group, then each group (treatment
level) consists of how many observations?
When we test H0: μ1 − μ2 0, HA: μ1 − μ2> 0, = 15.4, = 14.5, s1 = 2, s2 = 2.28, n1
= 35, and n2 = 18 at α = .01, can we reject the null hypothesis?
Failure to meet payments on student loans guaranteed by the US government has been a
major problem for both banks and the government. Approximately 50 percent of all
student loans guaranteed by the government are in default. A random sample of 350
loans to college students in one region of the United States indicates that 147 are in
default. Calculate the appropriate test statistic to test the hypothesis that the default rate
for the selected region is lower than the national percentage.
