Question 1

In order to plan transportation and parking needs at a private high school, administrators asked students how they get to school.  Some rode a school bus, some rode in with parents or friends, and others used "personal" transportation - bikes, skateboards, or just walked. The table summarizes the responses from boys and girls.
$\begin{array} { | l | c | c | c | } 
\hline& \text { Male } & \text { Female } & \text { Total } \
\hline \text { Bus } & 30 & 34 & \mathbf { 6 4 } \
\hline \text { Ride } & 37 & 45 & \mathbf { 8 2 } \
\hline \text { Personal } & 19 & 23 & \mathbf { 4 2 } \
\hline \text { Total } & \mathbf { 8 6 } & \mathbf { 1 0 2 } & \mathbf { 1 8 8 } \
\hline
\end{array}$

-What is the marginal distribution of gender?

Accepted Answer

The answer of In order to plan transportation and parking...

Question 2

Nickels minted in the United States are supposed to weigh 5.000 grams. Of course there is some variation in that. The actual weights are pretty well represented by a normal model with a mean of 5.000 g and a standard deviation of about 0.08 g. Draw and clearly label this model.

Accepted Answer

The answer of Nickels minted in the United States are...

Question 3

The best estimate of the standard deviation of the mens' weights displayed in this dotplot is 
A) 35
B) 40
C) 15
D) 10
E) 25

Accepted Answer

In this dotplot, there are 20 data points. Using the range rule of thumb, we can estimate the standard deviation as approximately the range of the data divided by 4.

The range of the data is roughly 100 - 60 = 40. Dividing by 4 gives an estimate of 10.

However, notice that there is one outlier at around 135. If we remove this outlier, the range becomes roughly 100 - 60 = 40. Dividing by 4 gives an estimate of 10.

So our best estimate for the standard deviation of the men's weights is around 10. However, based on the presence of the outlier, it might be more reasonable to use a slightly larger estimate of 15 or 25. Option E is the closest to our estimate of 10.

Question 4

The boxplots show fuel economy of 2011 model cars for the classes shown.  
a. Which class offers the car with the best gas mileage, and what is the mileage of that car?
b. Which class has the highest median gas mileage, and how much is it?
c. Which class of car has the smallest range of fuel economy, and what is it?
d. Which class of car has the smallest IQR, and what is it?
e. Which class of car generally gets the best mileage? Explain.

Accepted Answer

The answer of The boxplots show fuel economy of 2011...

Question 5

One thousand students from a local university were sampled to gather information such as gender, high school GPA, college GPA, and total SAT scores. The results were used to create histograms displaying high school grade point averages (GPA's) for both males and females. Compare the grade distribution of males and females.

Accepted Answer

The answer of One thousand students from a local university...

Question 6

The five-number summary for the fuel economy (in miles per gallon) of year 2011 midsize cars is:
$\begin{array}{|c|c|c|c|c|}
\hline Min & Q1 & Median & Q3 & Max \
\hline 13 & 21 & 23 & 26 & 50 \
\hline
\end{array}$
a. Would you expect the mean gas mileage of all midsize cars to be higher or lower than the median? Explain.
b. One model of Volkswagon gets 34 mpg, one model of Toyota gets 28 mpg, and one model of Bentley gets 13 mpg. Are any of these cars outliers? Explain.

Accepted Answer

The answer of The five-number summary for the fuel economy...

Question 7

The lifespans of a particular brand of graphing calculator are approximately normally distributed with a mean of 620 days from the purchase date and a standard deviation of 82 days. They will provide a warranty that guarantees a replacement if the calculator stops working within the specified time frame, and are trying to decide what time frame to use. a. If the company sets the warranty at a year and a half (say 540 days), what proportion of calculators will they have to replace?
b. The company does not want to have to replace more than 1% of the calculators they sell. What length of time should they set for the warranty?
c. The company would like to set the warranty for 540 days, and still replace no more than
1% of the calculators sold. Increasing the average life of the calculators is too expensive, but
they think they reduce the standard deviation of the lifespans. What standard deviation of lifespans would be needed to make this happen?
d. Explain what achieving a smaller standard deviation means in this context.

Accepted Answer

The answer of The lifespans of a particular brand of...

Question 8

Dimes minted in the United States average 2.286 g with a standard deviation of 0.06 g. A couple chemistry students were trying out their teacher's new scale by weighing a bunch of coins. The found a nickel that weighed 5.19 g and a dime that weighed 2.45 g. Which coin was more exceptionally heavy? Explain.

Accepted Answer

The answer of Dimes minted in the United States average...

Question 9

A professor has kept records on grades that students have earned in his class. If he wants to examine the percentage of students earning the grades A, B, C, D, and F during the most recent term, which kind of plot could he make?
A) pie chart
B) boxplot
C) dotplot
D) timeplot
E) histogram

Accepted Answer

A pie chart would be the best option for showing the percentage of students earning each grade, as it allows for easy comparison of the relative sizes of each category.

Question 10

To determine if people's preference in dogs had changed in the recent years, organizers of a local dog show asked people who attended the show to indicate which breed was their favorite. This information was compiled by dog breed and gender of the people who responded. The table summarizes the responses.
$\begin{array} { | c | c | c | c | } 
\hline& \text { Female } & \text { Male } & \text { Total } \
\hline \text { Yorkshire Terrier } & 73 & 59 & \mathbf { 1 3 2 } \
\hline \text { Dachshund } & 49 & 47 & \mathbf { 9 6 } \
\hline \text { Golden Retriever } & 58 & 33 & \mathbf { 9 1 } \
\hline \text { Labrador } & 37 & 41 & \mathbf { 7 8 } \
\hline \text { Dalmatian } & 45 & 28 & \mathbf { 7 3 } \
\hline \text { Other breeds } & 86 & 67 & \mathbf { 1 5 3 } \
\hline \text { Total } & \mathbf { 3 4 8 } & \mathbf { 2 7 5 } & \mathbf { 6 2 3 } \
\hline
\end{array}$
-Which of the W's are unknown for these data?

Accepted Answer

The answer of To determine if people's preference in dogs...

Question 11

In June 2003 Consumer Reports published an article on some sport-utility vehicles they had tested recently. They reported some basic information about each of the vehicles and the results of some tests conducted by their staff. Among other things, the article told the brand of each vehicle, its price, and whether it had a standard or automatic transmission. They reported the vehicle's fuel economy, its acceleration (number of seconds to go from zero to 60 mph), and its braking distance to stop from 60 mph. The article also rated each vehicle’s reliability as much better than average, better than average, average, worse, or much worse than average.
-Describe the W's, if the information is given:
· Who:
· What:
· When:
· Where:
· How:
· Why:

Accepted Answer

The answer of In June 2003 Consumer Reports published an...

Question 12

Owners of an exercise gym believe that a Normal model is useful in projecting the number of clients who will exercise in their gym each week. They use a mean of 800 clients and a standard deviation of 90 clients.
a. Draw and clearly label this model.

b. What is the first quartile of the weekly number of clients? [Show work]
c. An owner of another gym reports that 5% of the time their gym has fewer than 450 clients, and 40% of the time the gym has more than 1085 clients. What parameters should that owner use for his Normal model? N($\underline{\quad\quad}$ ,$\underline{\quad\quad}$ )

Accepted Answer

The answer of   Owners of an exercise gym...

Question 13

School administrators collect data on students attending the school. Which of the following variables is quantitative?
A) whether the student is in AP* classes
B) grade point average
C) whether the student has taken the SAT
D) class (freshman, soph., junior, senior)
E) none of these

Accepted Answer

Grade point average is a numerical value and therefore a quantitative variable. A) is categorical, C) is binary, and D) is ordinal. E) is not a valid option as one of the variables is quantitative.

Question 14

A research company frequently monitors trends in the use of social media by American Adults. The results of one survey of 1846 randomly selected adults looked at social media use versus age group. The table summarizes the survey results.
$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Age Group }$
$\text { Uses Social Media }\begin{array}{|l|c|c|c|c|r|}
\hline& 18-29 & 30-49 & 50-64 & 65+ & \text { Total } \
\hline \text { Yes } & 328 & 417 & 288 & 114 & \mathbf{1 1 4 7} \
\hline \text { No } & 67 & 125 & 265 & 242 & \mathbf{6 9 9} \
\hline \text { Total } & \mathbf{3 9 5} & \mathbf{5 4 2} & \mathbf{5 5 3} & \mathbf{3 5 6} & \mathbf{1 8 4 6}\\hline
\end{array}$
-Find each percent.
a) What percent of adults surveyed are social media users aged 30-49?
b) What percent of the social media users are aged 30-49?
c) What percent of adults aged 30-49 are social media users?

Accepted Answer

The answer of A research company frequently monitors trends in...

Question 15

Which of these variables is most likely to follow a Normal model?
A) hours of homework last week
B) number of cigarettes smoked daily
C) eye color
D) number of TV sets at home
E) head circumference

Accepted Answer

Head circumference is a physical characteristic that tends to follow a Normal distribution in a population.

Question 16

Repair bills An automobile service shop reported the summary statistics shown for repair bills (in $) for their customers last month. 
$\begin{array}{|l|r|}
\hline Min & 27 \
Q1 & 88 \
Median & 132 \
Q3 & 308 \
Max & 1442 \
Mean & 284 \
SD & 140 \
\hline
\end{array}$
a. Were any of the bills outliers? Show how you made your decision.
b. After checking out a problem with your car the service manager gives you an estimate of
"only $90." Is he right to imply that your bill will be unusually low? Explain briefly.

Accepted Answer

The answer of Repair bills An automobile service shop reported...

Question 17

Owners of a minor league baseball team believe that a Normal model is useful in projecting the number of fans who will attend home games. They use a mean of 8500 fans and a standard deviation of 1500 fans. Draw and clearly label this model.

Accepted Answer

The answer of Owners of a minor league baseball team...

Question 18

All students in a physical education class completed a basketball free-throw shooting event and the highest number of shots made was 32. The next day a student who had just transferred into the school completed the event, making 35 shots. Indicate whether adding the new student's score to the rest of the data made each of these summary statistics increase, decrease, or stay about the same.
a. mean
b. median c. range
d. IQR
e. standard deviation

Accepted Answer

The answer of All students in a physical education class...

Question 19

The Wechsler Adult Intelligence Scale - Revised (WAIS-R) follow a Normal model with mean 100 and
standard deviation 15. Draw and clearly label this model.

Accepted Answer

The answer of The Wechsler Adult Intelligence Scale - Revised...

Question 20

To determine if people's preference in dogs had changed in the recent years, organizers of a local dog show asked people who attended the show to indicate which breed was their favorite. This information was compiled by dog breed and gender of the people who responded. The table summarizes the responses.
$\begin{array} { | c | c | c | c | } 
\hline& \text { Female } & \text { Male } & \text { Total } \
\hline \text { Yorkshire Terrier } & 73 & 59 & \mathbf { 1 3 2 } \
\hline \text { Dachshund } & 49 & 47 & \mathbf { 9 6 } \
\hline \text { Golden Retriever } & 58 & 33 & \mathbf { 9 1 } \
\hline \text { Labrador } & 37 & 41 & \mathbf { 7 8 } \
\hline \text { Dalmatian } & 45 & 28 & \mathbf { 7 3 } \
\hline \text { Other breeds } & 86 & 67 & \mathbf { 1 5 3 } \
\hline \text { Total } & \mathbf { 3 4 8 } & \mathbf { 2 7 5 } & \mathbf { 6 2 3 } \
\hline
\end{array}$
-Find each percent.
a. What percent of the responses were from males who favor Labradors?
b. What percent of the male responses favor Labradors?
c. What percent of the people who choose Labradors were males?

Accepted Answer

The answer of To determine if people's preference in dogs...

Quiz 1: Stats Start Here

Nickels minted in the United States are supposed to weigh 5.000 grams. Of course there is some variation in that. The actual weights are pretty well represented by a normal model with a mean of 5.000 g and a standard deviation of about 0.08 g. Draw and clearly label this model.

The best estimate of the standard deviation of the mens' weights displayed in this dotplot is

A professor has kept records on grades that students have earned in his class. If he wants to examine the percentage of students earning the grades A, B, C, D, and F during the most recent term, which kind of plot could he make?

School administrators collect data on students attending the school. Which of the following variables is quantitative?

Which of these variables is most likely to follow a Normal model?

Owners of a minor league baseball team believe that a Normal model is useful in projecting the number of fans who will attend home games. They use a mean of 8500 fans and a standard deviation of 1500 fans. Draw and clearly label this model.

The Wechsler Adult Intelligence Scale - Revised (WAIS-R) follow a Normal model with mean 100 and standard deviation 15. Draw and clearly label this model.