Question 1

The two samples whose statistics are given in the table are thought to come from populations with
Equal variances. What is the pooled estimate of the population standard deviation? $$\begin{array} { | c | c | c | } 
\hline n & \text { Mean } & \text { SD } \
\hline 25 & 32 & 5 \
\hline 20 & 30 & 6 \
\hline
\end{array}$$

Accepted Answer

A)  5.46 
B)  1.64 
C)  5.50 
D)  5.59 
E)  3.32

Question 2

The Y-variable in a regression analysis is also known as the...

Accepted Answer

A)  response variable 
B)  predictor variable 
C)  independent variable 
D)  explanatory variable 
E)  none of these

Question 3

Investigators at an agricultural research facility randomly assigned equal numbers of chickens to be housed in two rooms. In one room, the chickens experienced normal day/night cycles, while in the other room lights were left on 24 hours a day to see if those chickens would lay more eggs. After collecting data for several days the researchers tested the hypothesis $\mathrm { H } _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ against the one-tail alternative and found $P = 0.22$. Which is true?

Accepted Answer

A)  The chickens in the lighted room averaged 0.22 more eggs per day 
B)  There's a 22% chance that there's really no difference in egg production. 
C)  There's a 22% chance another experiment will give these same results. 
D)  There's a 22% chance that chickens housed in a lighted room produce more eggs. 
E)  none of these

Question 4

A high school counselor was interested in finding out how well student grade point averages (GPA) predict ACT scores. A
sample of the senior class data was reviewed to obtain GPA and ACT scores. The data are shown in the table to the right. 
-Is there evidence of an association between GPA and ACT score? Test an appropriate
hypothesis and state your conclusion in the proper context.

Accepted Answer

The answer of A high school counselor was interested in...

Question 5

In 2010, the United Nations claimed that there was a higher rate of illiteracy in men than in women from the country of
Qatar. A humanitarian organization went to Qatar to conduct a random sample. The results revealed that 45 out of 234 men
and 42 out of 251 women were classified as illiterate on the same measurement test. Do these results indicate that the United
Nations findings were correct?
-Test an appropriate hypothesis and state your conclusion.

Accepted Answer

The answer of In 2010, the United Nations claimed that...

Question 6

A marketing company reviewing the length of television commercials monitored a random sample
Of commercials over several days. They found that a 95% confidence interval for the mean length
(in seconds) of commercials aired daily was (23, 27). Which is true?

Accepted Answer

A)  95% of the commercials they checked were between 23 and 27 seconds long. 
B)  Commercials average between 23 and 27 seconds long on 95% of the days. 
C)  95% of all the commercials aired were between 23 and 27 seconds a day. 
D)  95% of all samples would show mean commercial length between 23 and 27 seconds. 
E)  We're 95% sure that the mean commercial length is between 23 and 27 seconds.

Question 7

A biology professor reports that historically grades in her introductory biology course have
been distributed as follows: 15% A's, 30% B's, 40% C's, 10% D's, and 5% F's. Grades in her
most recent course were distributed as follows: $$\begin{array} { l | c | c | c | c | c } 
\text { Grade } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \
\hline \text { Frequency } & 89 & 121 & 78 & 25 & 12
\end{array}$$ 
a. Test an appropriate hypothesis to decide if the professor's most recent grade distribution
matches the historical distribution. Give statistical evidence to support your conclusion.
b. Which grade impacted your decision the most? Explain what this means in the context of
the problem.

Accepted Answer

The answer of A biology professor reports that historically grades...

Question 8

You could win a $1000 prize by tossing a coin in one of two games. To win Game A, you must get
Exactly 50% heads. To win Game B, you must get between 45% and 55% heads. Although which
Game you must play will be chosen randomly, then you may decide whether to toss the coin 20
Times or 50 times. How many tosses would you choose to make?

Accepted Answer

A)  It does not matter. 
B)  50 tosses for A, 20 tosses for B 
C)  50 tosses for either game 
D)  20 tosses for A, 50 tosses for B 
E)  20 tosses for either game

Question 9

In a local school, vending machines offer a range of drinks from juices to sports drinks. The
purchasing agent thinks each type of drink is equally favored among the students buying
drinks from the machines. The recent purchasing choices from the vending machines are
shown in the table. $$\begin{array} { | c | c | c | c | c | } 
\hline \text { Drink Type/Flavor } & \begin{array} { c } 
\text { Lemon Lime } \
\text { Sports Drink }
\end{array} & \begin{array} { c } 
\text { Kiwi } \
\text { Strawberry }
\end{array} & \begin{array} { c } 
\text { Tropical } \
\text { Punch }
\end{array} & \begin{array} { c } 
\text { Grape } \
\text { Sports Drink }
\end{array} \
\hline \text { Frequency } & 159 & 198 & 174 & 149 \
\hline
\end{array}$$ 
a. Test an appropriate hypothesis to decide if the purchasing agent is correct. Give
statistical evidence to support your conclusion.
b. Which type of drink impacted your decision the most? Explain what this means in the
context of the problem.

Accepted Answer

The answer of In a local school, vending machines offer...

Question 10

Test identification Suppose you were asked to analyze each of the situations described below. (NOTE: Do not do these problems!) For each, indicate which procedure you would use (pick the appropriate number from the list), the test statistic ( $z , t$, or $\chi ^ { 2 }$ "chi-squared"), and, if $t$ or $\chi ^ { 2 }$, the number of degrees of freedom. A procedure may be used more than once.

1. proportion - 1 sample
2. difference of proportions - 2 samples
3. mean - 1 sample
4. difference of means - independent samples
5. mean of differences - matched pairs
6. goodness of fit
7. homogeneity
8. independence 
a. Among randomly selected pets, 27% of the 188 dogs and 18% of the 167 cats had fleas.
Does this indicate a significant difference in rates of flea problems for these two pets?
b. Are there more broken bones in summer or winter? We get records about the number of
fractures treated in January and July at a random sample of 25 emergency rooms.
c. A random sample of 600 high school seniors reported their grade point averages and the
amount of financial aid offered them by colleges. We wonder if there is an association
between academic success and college aid.
d. For a random sample of 200 drivers at a gas station, we record the driver's gender (male
or female) and the type of gasoline purchased (regular, plus, or premium). We wonder if
there is an association between a driver's gender and the type of gasoline they buy.
e. The school newspaper wants a 95% confidence interval for the road test failure rate. In a
random sample of 65 student drivers, 37 said they failed their driver's test at least once.
f. A supermarket chain wants to know which of two merchandise display methods is more
effective. They randomly assign 15 stores to use display type A and 15 others to use display
type B, then collect data about the number of items sold at each store.
g. Tags placed on garbage cans allow the disposal of up to 30 pounds of garbage. A
random sample of 22 cans averaged 33.2 pounds with a standard deviation of 3.2 pounds.
Is this strong evidence that residents overload their garbage cans?

Accepted Answer

The answer of Test identification Suppose you were asked to...

Question 11

Flight costs Every year Educational Services (ETS) selects readers for the Advanced
Placement Exams. Recently the AP Statistics exam has been graded in Lincoln, Nebraska.
One objective of ETS is to achieve equity in grading by inviting teachers to be readers from
all parts of the nation. However budgets are a consideration also. The accountants at ETS
wonder if the flights from cities west of Lincoln are the same as flight costs from cities east
of Lincoln. A random sample of the expense vouchers from last year was reviewed for the
cost of airline tickets. Costs (in dollars) are shown in the table. $$\begin{array} { | c | c | } 
\hline \text { East } & \text { West } \
\hline 265 & 257 \
\hline 298 & 320 \
\hline 340 & 295 \
\hline 219 & 288 \
\hline 199 & 366 \
\hline 398 & 275 \
\hline 359 & 430 \
\hline 309 & 397 \
\hline 105 & 253 \
\hline 253 & 366 \
\hline
\end{array}$$ 
Indicate what inference procedure you would use to see if there is a significant difference
in the costs of airline flights between the west and east coasts to Lincoln, Nebraska, then
decide if it is okay to actually perform that inference procedure. (Check the appropriate
assumptions and conditions and indicate whether you could or could not proceed. You do
not have to do the actual test.)

Accepted Answer

The answer of Flight costs Every year Educational Services (ETS)...

Question 12

Every year favorite songs compete to be on a Top 200 list based upon sales and rankings by the experts in the music industry.
These songs have many characteristics, such as song length and beats per minute, which vary from category to category in
the music industry. A disc jockey wondered if the number of beats per minute in songs classified as dance music were lower
than the beats per minute in the songs that are ranked on a Top 200 list from 2001. A random sample of songs from each
group was selected and the beats per minute are listed in the chart at the right. Does this sample indicate that songs classified
as dance music have lower beats per minute than the songs ranked on a Top 200 list? 
-Create and interpret a 90% confidence interval.

Accepted Answer

The answer of Every year favorite songs compete to be...

Question 13

A San Jose State student collects data from 20 students. He compares the number of classes a student is enrolled in to their
GPA. Here are the results of the regression analysis. The conditions for inference are satisfied. 
-Find and interpret a 95% confidence interval for the slope of the regression equation.

Accepted Answer

The answer of A San Jose State student collects data...

Question 14

A total of 23 Gossett High School students were admitted to State University. Of those
students, 7 were offered athletic scholarships. The school's guidance counselor looked at their
composite ACT scores (shown in the tabl, wondering if State U. might admit people with
lower scores if they also were athletes. Assuming that this group of students is representative
of students throughout the state, what do you think? 
-Create and interpret a 90% confidence interval.

Accepted Answer

The answer of A total of 23 Gossett High School...

Question 15

Packing Line A packing company investigates hiring a national training consultant to
improve productivity on their packing line. The consultant is very expensive, so they will
only hire him if they are very sure that productivity will rise. The company hires the
consultant for a one-week trial to work with 18 employees before making a final decision
about the training program. The training program will be implemented if the average units
packed per employee increases by more than 10 cases per day. The company manager will
test a hypothesis using $$\alpha = 0.05$$ 
a. Write appropriate hypotheses (in words and in symbols).
b. In this context, which do you consider to be more serious - a Type I or a Type II error?
Explain briefly.
c. After this trial produced inconclusive results the manager decided to test the training
program again with another group of employees. Describe two changes he could make in
the trial to increase the power of the test, and explain the disadvantages of each.

Accepted Answer

The answer of Packing Line A packing company investigates hiring...

Question 16

A sports analyst was interested in finding out how well a football team's winning
percentage (stated as a proportion) can be predicted based upon points scored and points
allowed. She selects a random sample of 15 football teams. Each team played 10 games.
She decided to use the point differential, points scored minus points allowed as the
predictor variable. The data are shown in the table and regression output given below.

Accepted Answer

The answer of A sports analyst was interested in finding...

Question 17

The two samples whose statistics are given in the table thought to come from populations with
Equal variances. What is the pooled estimate of the population standard deviation? $$\begin{array} { | c | c | c | } 
\hline n & \text { Mean } & \text { SD } \
\hline 50 & 22 & 3 \
\hline 55 & 25 & 4 \
\hline
\end{array}$$

Accepted Answer

A)  3.50 
B)  3.56 
C)  1.87 
D)  5.00 
E)  3.52

Question 18

Doctors at a technology research facility randomly assigned equal numbers of people to use computer keyboards in two rooms. In one room a group of people typed a manuscript using standard keyboards, while in the other room people typed the same manuscript using ergonomic keyboards to see if those people could type more words per minute. After collecting data for several days the researchers tested the hypothesis $\mathrm { H } _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ against the one-tail alternative and found $P = 0.22$. Which is true?

Accepted Answer

A)  There's a 22% chance another experiment will give these same results. 
B)  none of these 
C)  The people using ergonomic keyboards type 22% more words per minute. 
D)  There's a 22% chance that there's really no difference in typing speed. 
E)  There's a 22% chance that people using ergonomic keyboards type more words per minute.

Question 19

Which of the following is true about Student's t-models?
I. They are unimodal, symmetric, and bell-shaped.
II. They have fatter tails than the Normal model.
III. As the degrees of freedom increase, the t-models look more and more like the Normal.

Accepted Answer

A)  I and III 
B)  I, II, and III 
C)  I only 
D)  II and III 
E)  I and II

Question 20

Auto repairs An insurance company hopes to save money on repairs to autos involved in
accidents. Two body shops in town seem to do most of the repairs, and the company
wonders whether one of them is generally cheaper than the other. From their files of
payments made during the past year they select a random sample of ten bills they paid at
each repair shop. The data are shown in the table. $$\begin{array} { | c | c | } 
\hline \begin{array} { c } 
\text { Bodies } \
\text { by Bock }
\end{array} & \begin{array} { c } 
\text { Velleman's } \
\text { Automagic }
\end{array} \
\hline 2130 & 2570 \
\hline 980 & 1120 \
\hline 3400 & 2950 \
\hline 2190 & 1880 \
\hline 1100 & 1660 \
\hline 1450 & 1700 \
\hline 4590 & 4030 \
\hline 3090 & 3970 \
\hline 1050 & 1130 \
\hline 2530 & 3660 \
\hline
\end{array}$$ 
Indicate what inference procedure you would use to see if there is a significant difference in the costs of repairs done at these two body shops, then decide if it is okay to actually perform that inference procedure. (Check the appropriate assumptions and conditions and indicate whether you could or could not proceed. You do not have to do the actual test.)

Accepted Answer

The answer of Auto repairs An insurance company hopes to...

Exam 6: Accessing Associations Between Variables

The Y-variable in a regression analysis is also known as the...

A marketing company reviewing the length of television commercials monitored a random sample Of commercials over several days. They found that a 95% confidence interval for the mean length (in seconds) of commercials aired daily was (23, 27) . Which is true?

Which of the following is true about Student's t-models? I. They are unimodal, symmetric, and bell-shaped. II. They have fatter tails than the Normal model. III. As the degrees of freedom increase, the t-models look more and more like the Normal.