We expect the average value of many sample means to be close to the population mean
from which they were drawn.
If you are a researcher and the purpose of the hypothesis test is to prove that your
findings are an improvement over the status quo, the condition that you are attempting
to prove is assigned to the null hypothesis.
Analysis of variance compares the variance between samples to the variance within
those samples to determine if means of populations are different.
Resampling is an example of a nonprobability sampling technique.
We can approximate the standard error of the proportion by substituting the sample
proportion, p, for the population proportion, p.
There is no interaction between Factors A and B when the data values for each level of
one factor behave in the same fashion across all levels of the other factor.
A convenience sample is an example of a nonprobability sample.
Suppose the average amount spent per shopper at the Super Fresh Grocery Store last
month was $46.10. A sample of 25 transactions from last month was randomly selected.
Another random sample of 50 transactions was also collected. We can be certain that
the sampling error from the sample of 50 customers will be less than the sampling error
from the 25 customers.
Because each observation from a sample for the sign test must be assigned a plus or
minus sign, this sampling distribution can be said to follow the binomial probability
distribution.
Two variables are dependent if changes in the levels of one variable do not affect the
levels of the other variable.
A stem and leaf display allows you to observe individual data values while a histogram
groups data values together.
The definition of the pth percentile (where p is any number between 1 and 100) is that
at least p percent of the observations will fall below the value of interest.
Failing to reject the null hypothesis and accepting the null hypothesis do not refer to the
same conclusion.
The equation used to calculate binomial probabilities relies on permutations of n objects
selected x at a time.
If the purpose of the regression model is to provide a prediction for the dependent
variable, the presence of multicollinearity provides unreliable results.
If you decide to use randomized block ANOVA and fail to reject the null hypothesis for
the main factor, you should perform a one-way ANOVA to be sure the blocking factor is
not covering up the difference in population means for the main factor.
A data set is known as a times series when each data point is associated with a specific
point in time.
All else being equal, a 90% confidence interval will be wider than a 95% confidence
interval.
Nominal data has all the features of interval data with the added benefit of having a true
zero point.
A common source of nonsampling errors is a survey that contains ambiguous questions
in the eyes of the respondent.
Parametric statistics describe procedures that assume that the population from which the
sample is drawn follows a known probability distribution.
Calculating the average time callers wait on the phone for technical support is an
example of inferential statistics.
The confidence level is a complement to the significance level.
A conditional probability is also known as a posterior probability, which is a revision of
the prior probability using additional information.
The ____________ criterion is described as the least pessimistic method and the one
with the lowest level of risk.
A) maximin
B) equally likely
C) minimax regret
D) maximax
The table below shows the number of cars sold last month by seven employees at
Concord Motors and their number of years of sales experience.
Management would like to test if the population Spearman rank-order correlation
coefficient is different than zero. The critical value for this test using α = 0.05 is
__________.
A) 0.600
B) 0.643
C) 0.786
D) 0.893
The following data represent the number of refrigerators sold for each of the past five
months for Templeton Appliances.
Using a two-period simple moving average, the mean absolute deviation is ________.
A) 2.5
B) 5.0
C) 7.5
D) 10.0
The sum of squares ________measures the variation between each data value and the
corresponding sample mean.
A) within
B) between
C) interaction
D) error
The table below shows the number of cars sold last month by seven employees at
Concord Motors and their number of years of sales experience.
Management would like to use simple regression analysis to estimate monthly car sales
using the number of years of sales experience. The test statistic for testing the
hypothesis that the population coefficient of determination is greater than zero is
________.
A) 2.21
B) 4.37
C) 7.92
D) 10.16
Scott has decided to invest in constructing and operating a new sandwich shop and
needs to decide how large to build this new facility. The annual profit, including the
depreciated investment, will depend on the demand for his products. The following
decision table shows the payoffs, in thousands of dollars, for various combinations of
facility size and demand along with Scott’s estimates for each demand level.
The expected monetary value, in thousands of dollars, for building a medium facility is
_______.
A) $36.00
B) $40.50
C) $46.00
D) $53.50
Use the information below to answer the following question(s).
The Marseille Water Taxi ferries tourists from the harbor at Marseille, France, to the
Frioul Islands in the Mediterranean Sea. The table below shows the number of
passengers on the noontime ferry over seven randomly selected days along with the
current ambient temperature in degrees Celsius.
Use the Marseille Water Taxi data to determine the 95% confidence interval for the
slope and interpret the results.
Use the following information to answer the question(s) below.
The National Football League has developed a regression model to predict the number
of wins during a season for a team using the following independent variables:
•Average points per game during the season (PPG)
•Average number of penalties committed per game during the season (PEN)
•Turnover differential during the season (TO)
Turnover differential is defined as the number of times the team took the ball away from
their opponent with a turnover minus the number of times the team gave the ball away to
their opponent with a turnover. For example, if TO = +5, the team had five more
takeaways than giveaways. If TO = “7, the team had seven more giveaways than
takeaways during the season.
The following Excel output shows the partially completed regression output from a
random season.
Which one of the following statements is true concerning the 95% confidence interval for
the regression coefficient for the PEN variable?
A) Because the confidence interval includes zero, we have evidence to conclude that there
is a relationship between the average number of penalties per game and the average
number of wins per season for a team.
B) Because the confidence interval includes zero, we have evidence to conclude that there
is no relationship between the average number of penalties per game and the average
number of wins per season for a team.
C) Because the confidence interval does not include zero, we have evidence to conclude
that there is a relationship between the average number of penalties per game and the
average number of wins per season for a team.
D) Because the confidence interval does not include zero, we have evidence to conclude
that there is no relationship between the average number of penalties per game and the
average number of wins per season for a team.
The Wall Street Journal reported that the average amount of time that a French person
spends eating lunch at a restaurant is 22 minutes. Perform a hypothesis test to determine
if a difference exists between the average time an American spends eating lunch when
compared to a person from France. The following data represents the time, in minutes,
that random French and American diners spent at lunch. Assume that the population
variances are equal.
The degrees of freedom for this hypothesis test are ________.
A) 9
B) 13
C) 14
D) 15
Assume that the number of customers who arrive at a water ice stand follows the
Poisson distribution with an average rate of 6.4 per 30 minutes. What is the probability
that three or four customers will arrive during the next 30 minutes?
A) 0.1888
B) 0.2365
C) 0.2884
D) 0.3517
The ________ probability distribution describes data where all the values have the
same chance of occurring.
A) discrete
B) normal
C) exponential
D) uniform
State University offers several sections of a Business Statistics course in an in-class and
online format. Both formats are administered the same final exam each year. You have
been assigned to test the hypothesis that the average final exam score of in-class
students is different from the average final exam score of online students. The following
data summarizes the sample statistics for the final exam scores for students from each
format. Assume that the population variances are unequal.
If Population 1 is defined as in-class format and Population 2 is defined as online
format, and using α = 0.05, the conclusion for this hypothesis test would be because the
absolute value of the test statistic is
______________________________________________________________.
A) less than the absolute value of the critical value, you can conclude that the average
final exam score of in-class students is equal to the average final exam score of online
students
B) less than the absolute value of the critical value, you cannot conclude that the
average final exam score of in-class students is different from the average final exam
score of online students
C) more than the absolute value of the critical value, you cannot conclude that the
average final exam score of in-class students is different from the average final exam
score of online students
D) more than the absolute value of the critical value, you can conclude that the average
final exam score of in-class students is different from the average final exam score of
online students
Exponential smoothing with trend adjustment is a technique that compensates an
exponential smoothing forecast for any trend detected in the data.
Chris is a photographer and sells two types of photography for consignment in an art
store landscapes and flower close-ups. She also sells each in three print sizes 8×10,
11×14, and 13×19 inches. The following table shows the number of prints of each type
and size that have recently sold.
Construct a contingency table for this data.
Consider the following frequency distribution.
Which rule for constructing a frequency distribution using grouped quantitative data has
been violated?
A) Use equal-size classes.
B) Use mutually exclusive classes.
C) Avoid empty classes.
D) No rule has been violated.
Use the information below to answer the following question(s).
Some research has indicated that as people age they need less sleep. A random sample
of adults was selected and the number of hours that they slept last night was recorded.
Simple regression analysis was performed on this sample and the results are shown
below.
Which one of the following statements is true using α = 0.10?
A) Because the p-value for the slope is 0.065, we can reject the null hypothesis and
conclude that there is a relationship between the hours of sleep and the age of the adult.
B) Because the p-value for the slope is 0.065, we fail to reject the null hypothesis and
conclude that there is a relationship between the hours of sleep and the age of the adult.
C) Because the p-value for the slope is 0.065, we can reject the null hypothesis and
conclude that there is no relationship between the hours of sleep and the age of the
adult.
D) Because the p-value for the slope is 0.065, we fail to reject the null hypothesis and
conclude that there is no relationship between the hours of sleep and the age of the
adult.
The following distribution shows the frequency distribution of the number of shots a
particular NBA player blocked in one game for a random sample of 100 games.
You have been assigned the task to test if the distribution of blocked shots per game for
this player follows the Poisson distribution using α = 0.05. The expected number of
games from this sample that this player blocks exactly one shot is ________.
A) 19.31
B) 21.52
C) 22.38
D) 25.65
The following data represent a random sample the golf scores for a particular golfer
from a course that he regularly plays.
This golfer would like to test if his golf scores at this course follow the normal
probability distribution with μ = 85.0 and σ = 5.0 using α = 0.05. The degrees of
freedom for the critical value is ________.
A) 3
B) 4
C) 5
D) 6
The Canadian government would like to test the hypothesis that the standard deviation
for the hourly wage for men is equal to the standard deviation for the hourly wage for
women. The following data summarizes the sample statistics for hourly wages for men
and women.
The correct hypothesis statement would be ________________.
A)
B)
C)
D)
The ________ measures the variation in the dependent variable that is explained by
variables other than the independent variable in simple regression analysis.
A) sum of squares within
B) sum of squares error
C) sum of squares regression
D) total sum of squares
Which one of the following statements about probability is not true?
A) The probability of any event must range from 0 to 1.
B) If P(A) = 1, then with certainty, Event A must occur.
C) If Events A and B are mutually exclusive, then Event A or Event B must occur.
D) If P(A) = 0, then with certainty, Event A will not occur.
Suppose the average math SAT score for students enrolled at Madison College is 507.3
with a standard deviation of 68.2. A random sample of 43 students has been selected.
The standard error of the mean for this sample is ________.
A) 7.1
B) 10.4
C) 38.4
D) 68.2
Bananas are sold in bunches at a grocery store and typically consist of 4-8 bananas per
bunch. Suppose the weight of these bunches follows a normal distribution with a mean
of 3.54 pounds and a standard deviation of 0.63 pounds. The interval around the mean
that contains 99.7% of the bunch weights is ________.
A) 2.28, 4.80
B) 1.65, 5.43
C) 1.02, 6.06
D) 0.39, 6.69
The median is the ________ percentile in the data set.
A) 25th
B) 50th
C) 75th
D) 100th
The Centers for Disease Control (CDC) would like to test the hypothesis that the
proportion of obese adults in the U.S. has increased this year when compared to last
year. A random sample of 125 adults this year found that 56 were obese. Last year, a
random sample of 140 adults found that 42 were obese. If Population 1 is defined as
this year and Population 2 is defined as last year, which one of the following statements
is true?
A) Because the 98% confidence interval does not include zero, the CDC cannot
conclude that the proportion of obese adults in the U.S. has increased this year when
compared to last year.
B) Because the 98% confidence interval does not include zero, the CDC can conclude
that the proportion of obese adults in the U.S. has increased this year when compared to
last year.
C) Because the 98% confidence interval includes zero, the CDC cannot conclude that
the proportion of obese adults in the U.S. has increased this year when compared to last
year.
D) Because the 98% confidence interval includes zero, the CDC can conclude that the
proportion of obese adults in the U.S. has increased this year when compared to last
year.
A ________is a graph showing the number of observations in each class of a frequency
distribution.
A) frequency distribution
B) polygon
C) relative frequency distribution
D) histogram
A ________ sample is a sample in which each member of the population has a known,
nonzero, chance of being selected for the sample.
A) systematic
B) simple random
C) probability
D) convenience
Suppose the average tread-life of a certain brand of tire is 42,000 miles and that this
mileage follows the exponential probability distribution. What is the probability that a
randomly selected tire will have a tread-life of less than 65,000 miles?
A) 0.3084
B) 0.4497
C) 0.5630
D) 0.7872
Suppose the local Best Buy store averages 483 customers per day entering the facility
with a standard deviation of 112 customers. A random sample of 48 business days was
selected. What is the probability that the average number of customers in the sample is
between 480 and 500?
A) 0.1579
B) 0.2521
C) 0.3377
D) 0.4284
The airline industry defines no-shows as passengers who have purchased a ticket but
fail to arrive at the gate on time for departure. Southwest Airlines operates many flights
from Philadelphia to Dallas and experienced the following no-show probability
distribution last year.
The following data represent the number of no-shows that occurred on a random sample
of 120 flights between these two cities this year.
Southwest Airlines would like to know if the probability distribution of no-shows has
changed between last year and this year on flights between these two cities using α =
0.05. The degrees of freedom for the critical value is ________.
A) 3
B) 4
C) 5
D) 6
Assume that the number of pieces of junk mail per day that a person receives in their
mail box follows the Poisson distribution and averages 4.3 pieces per day. What is the
probability that this person will receive exactly seven pieces of junk mail over the next
two days?
A) 0.1271
B) 0.1812
C) 0.2355
D) 0.2924
The following data shows the number of students that came to office hours per day for a
particular faculty member.
Construct a cumulative relative frequency distribution for this data and determine the
probability that fewer than three students will come to office hours today.
Historically, voter turnout for political elections in Texas have been reported to be 54%.
You have been assigned by a polling company to test the hypothesis that voter turnout
during the most recent election was higher than 54%. You have collected a random
sample of 90 registered voters from this elections and found that 54 actually voted. Use
the critical value approach to test this hypothesis with α = 0.02.
Note: The problems below use the following information:
The following data show the minutes that randomly selected flights were delayed from
their scheduled departure at three different airports throughout different time intervals
during the day.
If appropriate, perform a multiple comparisons test to determine which counties are
different in terms of the average number of hours worked per week using α = 0.05.
Zappos is an online retailer based in Nevada and employs 1,300 employees. One of
their competitors, Amazon.com, would like to test the hypothesis that the standard
deviation for the age of Zappos employees equals 6.0 years. The ages from a random
sample of 16 Zappos employees were recorded and found to have a standard deviation
of 5.3 years. Test this hypothesis using α = 0.10.
According to a recent survey conducted by Country Financial, 58% of adults 18 and
older felt that a college education was still a good financial investment. To verify these
results, a random sample of 210 adults was selected of which 142 felt that a college
education was still a good financial investment. Does this sample support the findings
of Country Financial?
Use the following information to answer the question(s) below.
The following data provides the monthly Comcast cable bill for a random sample of 20
households along with the number of televisions in the household (TV), the number of
people living in the household (People), and the number of years that household has
been a Comcast customer (Years).
Construct a 95% confidence interval to estimate the average monthly cable bill for a
household that has three televisions, has four people in the household, and has been a
Comcast customer for 10 years.
According to IDC, Samsung controls 19.0% of the smartphone market. A random
sample of three was selected. Determine the probability that the first two phones are
Samsung and the third phone is not.
The pH scale measures the amount of alkalinity or acidity in a liquid and ranges from 0
to 14. The ideal pH for a swimming pool is 7.2. A pH that is too high or low can cause
discomfort for the swimmers, especially in the eyes. Chemicals need to be added to the
water to adjust the pH to the desired level. Fifteen pH readings were taken at the Wilson
Community Pool from different locations at 10 am this morning. The average pH
reading from this sample was 7.02 with a standard deviation of 0.40. Using α = 0.05
and the critical value approach, determine if corrective action is needed at this pool to
adjust the pH value.