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understand all
solutions before taking your exam.
1 . a. The type of study is observational with the variable of
interest being the
age of the student.
2 . (41.1, 50.9)
3. a. 36 movies
b . 29 movies
c. 23 movies
d. About 230 minutes
4. Part a: Median 139,500 Mean: 163,125
Part b: Outlier 34,000 Median: 140,000 Mean: 182, 000
Part c: outlier 434,000 Median: 139,000 Mean: 124,428.57
5 . a. The goal is to determine how many teachers would choose
a different
career if given the opportunity
b . All US teachers
c. Percentage of teachers who would choose a different career
d. 2150 teachers who were questioned
e . Raw data is teacher responses (yes no) to question if they
would choose a
different career.
f. 60% of teachers who said they would choose a different
career

g. 55%---65%
6. Red: (0.85,0.97)
Yellow: (0.86, 0.98)
Blue: (0.86,0.94)
7 . F ro m st at di sk
Source: DF: SS: MS: Test Stat, F: Critical F: P---Value:
Treatment: 2 0.00224 0.00112 0.505269 6.112108 0.612123
Error: 17 0.03769 0.002217
Total: 19 0.03993
Fail to Reject the Null Hypothesis
There is not sufficient evidence to reject equality of means
The p value 0.61
We have sufficient evidence to claim the mean of all colors is
the same.
8. Expected probability of rolling a 2: 0.16
Actual results: 0.44
Difference 0.28, this is statistically significant
9 . Null hypothesis: The mean of all three players are the same
Alternative hypothesis: the mean of at least one player is
different
The p value is 0.036
At this level we must reject Ho and conclude at least one mean
is statistically
different.
1 0 . The minimum sample size is 365 students
1 1 . a. 58%

b . 74%
c. 82%
d . 7 8
1 2 . H0: p=0.095
a. Ha: P<---.095
b . P hat= 0.0920
c. Z=---0.33
d. No
Test results from stat disk are as follows:
Claim: p < p(hyp)
Sample proportion: 0.0920304
Test Statistic, z: ---0.3288
Critical z: ---1.6449
P---Value: 0.3712
90% Confidence interval:
0.0773847 < p < 0.106676
Sample does not provide enough evidence to support the claim
1 3 . a. 2 standard deviations
b . 97.72%
1 4. FROM STAT DISK:
Descriptive Statistics
Column 3
Sample Size, n: 15
Mean:8.2

Median: 8
Midrange: 8.5
RM S : 8.306624
Variance, s^2: 1.885714
St Dev, s:1.373213
Mean Abs Dev: 1.066667
Range: 5
Coeff. Of Var. 16.75%
Minimum: 6
1 st Quartile: 7
2 nd Quartile: 8
3 rd Quartile: 9
Maximum: 11
Sum: 123
Sum Sq: 1035
c. The best estimate for the mean is 8.2 people
d. The 95% confidence interval is (from stat disk)
Margin of error, E = 0.7586815
95% Confident the population mean is within the range:
7. 44 1 3 1 9 < mean <8.958681
No this is not representative of the entire nation
1 5 . Type I error: reject the fact that males and females are
equal in GPA when
that is in fact true
Type II error--- Conclude the GPA of males and females are
equal when that is
not in fact true

1 6. (97.22,107.78)
1 7. From stat disk we have:
7 7 .4 8 0 0 9 < mean <82.51991
1 8 . A. Null hypothesis: Survey response is independent of
gender
Alternative hypothesis: There is a relationship between survey
response
and if the respondent has children
b .
Y e s N o
Has Children 177.523 252.477
Does not 47.477 67.523
c . 7 . 1 0 3
d . 3 . 8 4
e . The data supports the alternative hypothesis.
1 9 . a. 57th percentile
b . 5th percentile
c. 85th percentile
2 0 .
Number Frequency Relative

frequency (as a
Cumulative
frequency
%)
1 2 16.7% 2
2 3 25% 5
3 2 16.7% 7
4 2 16.7% 9
5 1 8.3% 10
6 2 16.7% 12
2 1 . a. 16
b. 2.5%
c . 81.5 %
2 2 . a Quantitative, discrete, ratio
b . Quantitative, continuous, ratio
2 3 . a. ---3 percentage points
b . ---4 2 . 9 %
2 4. a. Mean=1518 standard deviation=32.5
b . Mean= 1518 standard deviation= 29.5
2 5 . H0: μ=0.3
Ha : μ<0.3
B. t=---0.119
c. The data supports the null hypothesis
2 6. a. 10.4
b . Less than 0.0001
2 7 . From Stat disk:
Sample size, n: 8

Degrees of freedom: 6
Correlation Results:
Correlation coeff, r: 0.6652373
Critical r: ±0.706734
P---value (two---tailed): 0.07182
Sample does not provide enough evidence to support a linear
correlation
Regression Results:
Y= b0 + b1x:
Y Intercept, b0: 361.9401
Slope, b1: 18.20297
Total Variation: 7.497885e+6
Explained Variation: 3.318119e+6
Unexplained Variation: 4.179766e+6
Standard Error: 834.6423
Coeff of Det, R^2: 0.4425406
2 8 . Margin of error: 2.0 confidence interval (73,77) if using
formula from book
Or from stat disk
73.01579 < mean <76.98421
2 9 . McGwire: Range: 120 Standard deviation 3 9.00
So sa: Range 90 Standard deviation 31.9

3 0 . Sample--- 1025 randomly selected adults
Population: all adult Americans
Sampling method: simple random sampling
Sample statistic: 47% who believe the best years are ahead
Population parameter: Amount of all Americ ans who believe
the best years
area ahead of us
This sample is likely representative of the population due to the
fact it is
randomly selected and more than 1000 people are chosen
Please take the time to review the following mathematical
problems. If you have are
able to solve these problems you will be in GOOD shape for
your final exam.. You
may check your solutions at the end of this document.
Remember you only have ONE attempt at the final exam MAKE
IT COUNT!
Your exam is open note and open book please take advantage of
the opportunity to use
these resources
1. An admissions advisor for a local college decides he would
like to determine

the average age of students at the college for some promotional
materials. To
do this he pulls the records of 200 random students at the
college.
What type of study is this (observation or experiment), what is
the variable
of interest?
2. Fifty registered nurses are asked how many hours they work
each week.
Based on this sample the estimated average is 46 hours with a
margin of
error of 4.9 hours. Use the given values to identify the
confidence interval
likely to contain the actual population mean.
3. The following histogram represents the movie lengths hit
movies in 1998
a How many movies total are represented in this histogram?
b. How many movies lasted less than 150 minutes?
c. How many movies lasted more than 120 minutes?
d. What is the highest possible movie length represented in this
histogram?

4. A real estate agent records the price of the eight homes she
has listed at this
moment they are as follows:
123,000 155,000 139,000 140,000 159,000 34,000
121,000 and
434,000
a. Find the mean and median of the data presented
b. Identify the outlier on the LOW end of the data set, remove
this value
and calculate the new mean and median
c. Identify the outlier on the HIGH end of the data set, remove
this value
what is the new mean and median of the data set (HINT be sure
you
put your low value back in!)
5. In a survey of 2,150 teachers it was found that 60% of them
said if they could
start their careers again they would choose a different career.
The margin of
error was 5 percentage points
What was the goal of this study
What is the population
Identify the population parameter of interest
Identify the sample
What is the raw data collected for this study
Identify the sample statistic
Based on the margin of error identify the range of values likely

to contain
the population parameter of interest
6. The following table shows the average weight and standard
deviation for
different colored M and M’s in grams
Color Mean Standard deviation
Red 0.91 0.03
Yellow 0.92 0.03
Blue 0.90 0.02
Assume the machine filling the bag is set to reject M and M’s
more than 2
standard deviations above and below the mean
For each color find the range of weights that are acceptable to
the vending
machine
Red:
Yellow:
Blue:
7. The following table measures the weight of M and M’s (in
grams) of various
colors of the candy.
Orange Blue Green
0.903 0.838 0.911
0.92 0.875 1.002
0.861 0.87 0.902
1.009 0.956 0.93
0.971 0.968 0.949
0.898 0.89
0.942 0.902
0.897
Use a 0.01 level of significance to test the claim that the
different colors all

have the same mean.
a. Find the p value
b. At this level is there significant evidence to say that all
colors have the
same mean?
8. A statistics student decided to roll a dice 25 times, she rolled
the number two
11 times. Is the difference between what the student had occur
and what is
expected statistically significant?
9. Data was recorded for the number of home runs hit for three
baseball
players, Mark McGwire, Sammy Sosa and Barry Bonds. The
Analysis of
Variance results obtained from software are found below. The
significance
level is 0.10 in testing the null hypothesis.
Source: DF: SS: MS: Test Stat Critical
F: P-Value:
Treatment: 2 9546.87 4773.43 3.35 2.32
0.036
Error: 206 293224.08 1423.41
Total: 208 302770.95
What is the null hypothesis?
What is the alternative hypothesis
What is the p value
Is there sufficient evidence to support the claim that the three
players have

different average number of home runs hit?
10. A researcher wishes to estimate the average number of
hours that high
school students spend on facebook each day. A margin of error
of 0.22 hours
is desired. Past studies suggest a population standard deviation
of 2.1 hours
is reasonable, estimate the minimum sample size needed to
estimate the
population mean with the desired accuracy.
11. A study was done among 1200 Walden Students. Among
these students 700
were Masters of Nursing students and 520 of these were taking
their first
online course. Among the 500 other students, 410 were taking
their first
online course.
a. What percentage of students were nursing students
b. What percentage of nursing students were taking their first
online
course
c. Among those who were NOT nursing students what
percentage were
taking their first online course?
d. What percentage of the students were taking the first online
course?
12. On research study of illegal drug use among teenagers
shows a decrease from

11.4% in 1997 to 9.5% now. Suppose a study in a large high
school reveals
that in a simple random sample of 1054 students 97 report using
illegal
drugs. Use the 0.05 significance level to test the principal’s
claim that illegal
drug use is below the national average.
a. formulate the null and alternative hypothesis
b. The sample statistics are the sample size n=1054 and the
sample
proportion , find the sample proportion rounded to four decimal
places
c. Find the standard score, z for the sample proportion
d. Is there sufficient evidence to support the principals claim
that the
illegal drug use at this school is below the national average?
13. Suppose you know the distribution of sample proportions in
samples of 300
registered voters who will vote for candidate A is normal with
a mean of
0.34 with a standard deviation of 0.02. Suppose you select a
random sample
of 300 voters and find the proportion of those willing to vote
for candidate A
is 0.38.
a. How many standard deviations is the sample proportion from
the
mean of the distribution of sample proportions?
b. What is the probability the selected sample would have a

proportion
of less than 0.38?
14. You select a random sample of n=15 families in your
neighborhood and find
the following family sizes.
7
8
11
10
9
7
8
8
7
8
7
8
9
10

6
Find the mean family size from the sample as well as the
standard deviation
What is the best estimate for the mean sample size for the
population of all family sizes in the country?
What is the 95% confidence interval for the mean?
Do you feel this sample is representative of the entire nation
why or why not?
15. Given the following hypothesis statements:
Ho: The average GPA of males=average GPA of females
Ha: The average GPA of males is not equal to the average GPA
of females
Explain in the context of GPA for males and females what it
means to make a
type I and type II error.
16. A simple random sample of 25 student IQ scores is selected.
The average
score is 102.5 with a standard deviation of 12.8. Us the t
distribution to
construct a 95% confidence interval for the population mean.
17. Assume that the population mean is to be estimated from a
sample. Use the
sample results to approximate the margin of error and 95%
confidence level.
Sample size=121 sample mean=80 sample standard deviation

=14
18. A simple yes/no survey is presented to two groups of
subjects, those with
children and those without. The results are summarized in the
two way table
below.
Yes No
Respondent has children 190 240
Respondent does not
have children
35 80
a. State the null and alternative hypotheses
b. Find the table of expected frequencies
c. Find the chi squared test statistic
d. Find the critical value of the chi squared test statistic at a
0.05 level of
significance
e. Based on these values which hypothesis is supported?
19. In a recent study of 353 4 year old girls the following data
was collected:
One of the girls weighed 40 pounds, she was heavier than 200
of the other
girls. What percentile is this value?
One of these girls weighed 24 pounds, she was heavier than 18
of the other
girls, what percentile was this particular value?
One of the girls weighed 44 pounds and was heavier than 301 of

the other
girls. What is the percentile of this particular value?
20. A high school student rolls a dice 12 times and records the
following results
1 4 6 2 2 3 4 5 6 1 2 3
Based on these results complete the following table (round to
the nearest
tenth as needed)
Number Frequency Relative
frequency (as a
%)
Cumulative
frequency
1
2
3
4
5
6
21. Assume the average weight of 5 year olds is normally
distributed with a
mean of 45 pounds and standard deviation of 5 pounds. Using
the 68-96-
99.7 rule find the following:
a. Percent of five year olds who weigh less than 40 pounds
b. The percent who weigh more than 55 pounds
c. The percent who weigh between 40 and 55 pounds

22. Determine if the following variable is qualitative or
quantitative and give
their level of measurement. If it is quantitative in nature stat if
it is
continuous or discrete.
Number of facebook friends
Weight in pounds
23. The amount of income people save on average has
decreased from 7% to
4%.
a. The savings rate has decreased by ____ percentage points
b. Find the percent change in savings rate
24. Based on data from the college board assume SAT scores
are normally
distributed with a mean of 1518 points an d a standard deviation
of 325
points.
a. If a sample of 100 students is taken find the mean and
standard
deviation of the distribution of sample means
b. If a sample of size 121 students is taken find the mean and
standard
deviation of the distribution of sample means
25. A simple random sample of 16 different cereals is
obtained; the sugar
content (in grams) is measured for each cereal. The sample has
a mean of

0.295 grams, a standard deviation of 0.168 grams. Use the 0.05
level of
significance to test the claim that the mean amount of sugar is
less than 0.3
grams.
a. State the null and alternative hypothesis statements
b. Find the test statistic T
c. Which hypothesis does the data support?
26. A random sample of thirty six cans of cola has a mean of
12.19 ounces with a
standard deviation of 0.11 ounces. Assume we are using a 0.05
level of
significance to test the hypothesis the average can of cola
contains more than
12 ounces.
a. Find the test statistic z
b. Find the p value
27. The following data set includes the selling prices of
homes (in thousands)
and the amount of taxes paid
Selling Taxes
142 3167
175 4033
129 1471
138 3204
232 3513
135 3028
150 3131
207 5158
Find the r and r squared values

28. A population mean is to be estimated from the sample
described below.
Find the margin of error and 95% confidence interval.
Sample size 100, sample mean 75.0 sample standard deviation
10.0
29. The following table gives the homerun distances of ten
home runs hit by
Sammy Sosa and Mark McGwire. Find the range and standard
deviation for
each player
McGwire Sosa
360 371
370 350
370 430
430 420
420 430
340 434
460 370
410 420
440 440
410 410
30. In a Gallup poll targeting 1025 randomly selected adult
Americans 47%
believed that the nations best years were still ahead of us
(rather than
behind us). Identify the following:

a. The sample
b. The population
c. The sampling method used
d. Identify the sample statistic
e. Identify the population parameter
f. Do you believe the sample is representative of the
population? Why?

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