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Name ________________________
AP Statistics
Date ___________________
Schwimmer
Midterm Review #4
1.
Following are the combined scores for two weeks of NFL games. For instance, in the
first game, the teams scored a combined 32 points.
(a) Find the mean and the median of the data set.
x  42.5, median = 40.5
(b) Based on the values you get in (a), what can you say about the shape of the
distribution? Explain.
The distribution is slightly skewed to the right. This is because the mean is larger
than the median. The mean is pulled towards the higher values.
(c) Are there any outliers in this data set? Show your work.
IQR  Q3  Q1  48.5  35  13.5
13.5 1.5  20.25
Q1  20.25  14.75
Q3  20.25  68.75
2.
An observation would be considered an
outlier if it was less than 14.75 or greater
than 68.75.
There are two outliers of 72 and 79.
(a) A teacher gave an exam and created a stemplot of the grades in terms of percents.
Which is the largest?
(1)
(2)
(3)
(4)
the mean
the median
the mean and median are the same
impossible to tell
(b) The teacher decides to curve the exams by adding 5 percentage points to each grade.
So, a 67% turns into a 72%. Which of the following would change?
(1) the range
(2) the standard deviation
(3) both the range and standard deviation
(4) neither the range nor the standard deviation
(c) The teacher changes his mind and decides to curve the grades in another way. He
takes the square root of the grade. For instance, an 81% will change to a 90%. What will
happen to the standard deviation of the curved grades?
(1) It will go up.
(2) It will go down.
3.
(3) It will stay the same.
(4) It is impossible to tell.
The busiest season for Walmart is the Christmas season. Holiday and weekends see a
tremendous number of customers. Last year, Walmart conducted a study as to the
amount of waiting time in checkout lanes its customers had to wait. On Saturdays and
Sundays of its holiday season, it opened a different number of checkout lanes for
customers between 1PM and 4PM, its busiest times. The measurement was the average
wait time for a customer to go through the lane and complete the transaction. A different
number of lanes was opened each day. The data is below.
(a) What is the explanatory variable? What is the response variable?
The explanatory variable is # of lanes open
and the response variable is average wait time.
(b) Make a scatterplot on the grid provided.
(c) There is a clear outlier on the scatterplot.
Circle it.
(d) Give a reason that would justify eliminating
the outlier.
It snowed that day, so the store probably
wasn’t as busy as usual.
(e) Generate the least squares regression line that describes the data (with the outlier
eliminated).
predicted wait time  14.9621  .9627# of lanes open 
(f) Interpret the slope of the LSRL in context.
slope =  .9627  wait time
1
# of lanes open
For every one additional lane that is opened,
you are expected to wait .9627 minutes less.
(g) What specific point is the LSRL guaranteed to go through?
Every LSRL goes through the point x, y .
The point for this line would be (8.4545, 6.8227).
(h) Find the value of r and interpret it in context.
r = –.8821
There is a fairly strong, negative, linear association between
average wait time and # of lanes open.
(i) Find the value of r2 and interpret it in context.
r 2  .778
77.8% of the variation in average wait time is explained by the
least squares regression line.
(j) What is the difference between the actual waiting time and predicted waiting time for
7 lanes? What is this value called?
Residual = observed – predicted
predicted wait time  14.9621  .96277 
predicted wait time  8.2232
Residual = 6.75 – 8.2232 = –1.4732
(k) What is the predicted average waiting time if Walmart opens only one lane? Why
does this answer make little sense for this problem?
predicted wait time  14.9621  .96271  13.9994
This value makes little sense because it is extrapolation.
4.
A preliminary study conducted at a medical center in St. Louis has shown that treatment
with small, low-intensity magnets reduces the self-reported level of pain in polio patients.
During each session, a patient rested on an examining table in the doctor’s office while
the magnets, embedded in soft pads, were strapped to the body at the site of pain.
Sessions continued for several weeks, after which pain reduction was measured.
A new study is being designed to investigate whether magnets also reduce pain in
patients suffering from herniated disks in the lower back. One hundred male patients are
available for the new study.
(a) Describe an appropriate design for the new study. Your discussion should briefly
address treatments used, methods of treatment assignment, and what variables would
be measured. Do not describe how the data would be analyzed.
Have the men report their pain level rating prior to receiving treatment. Put all the
names of the men into a hat and pick names out. The first 50 men should go into
treatment group 1. The remaining 50 men should go into treatment group 2. The first
treatment group should use the magnets on the site of pain. The second treatment
group should use “placebo” magnets on the site of pain. To reduce potential bias in
the experiment, this study should be double-blind so neither the patients nor the
administers of the treatment know which magnets are real. After the treatments are
given, the men will be asked to rate their level of pain again. We will compare the
difference in pain ratings from before and after.
(b) Would you modify the design above if, instead of 100 male patients, there were 50
male and 50 female patients available for the study? If so, how much would you
modify your design? If not, why not?
If you think that males and females may react differently to the treatment of magnets,
then we could block on gender. We would randomly assign 25 women into treatment
group 1 and 25 women into treatment group 2 (as we did above) and do the same for
men. Only compare women’s difference in pain ratings to women and men to men.
If you think that gender makes no difference in reaction to the treatment of magnets,
then you shouldn’t make any changes in your experiment design.
5.
Credit card balances for young couples are roughly normally distributed and have a mean
of $750 and a standard deviation of $265.
(a) What is the probability that a typical couple’s balance is more than $1,000?
1000  750 

P( x  1000)  P z 
  P( z  .9434)  .1727
265


Draw a curve also!!!
(b) What is the probability that the average balance of an SRS of 5 couples is more than
$1,000?
 x    750

265
x 

 118.512
n
Draw a curve!!
5
1000  750 

P( x  1000)  P z 
  P( z  2.11)  .0174
118.512 

6.
The average number of years that a particular washing machine lasts is 7.45 years with a
standard deviation of 2.71 years. Assume normality. The warranty for this machine is
two years.
You should draw an appropriate normal curve for each of these exercises.
(a) What is the probability that a machine will last more than 8 years?
8  7.45 

P( x  8)  P z 
  P( z  .203)  .4196
2.71 

(b) What is the probability that an SRS of 100 washing machines will average a lifetime
of 8 or more years?
 x    7.45

2.71
x 

 .271
n
100
8  7.45 

P( x  8)  P z 
  P( z  2.03)  .0212
.271 

(c) What is the probability that a machine will fail within the warranty period?
2  7.45 

P( x  2)  P z 
  P( z  2.011)  .0222
2.71 

(d) What is the probability that an SRS of 15 will average failing within the warranty
period?
 x    7.45

2.71
x 

 .271
n
100
2  7.45 

P( x  2)  P z 
  P( z  5.45)  0
.271 
