MATH
1
6
Elementary Statistics
Monterey Peninsula College
Student Name Date Score
Final Exam – Part #1
Chapters 1 through 10, 1
2
: Descriptive and Inferencial Statistics, Probability
Distributions, Linear Regression and Analysis of Variance
Solve the following problems and choose the right answer. Show your work!
1. (1 point) The following table gives the frequency distribution for the years a President of
the United States lived after first ianuguration. Verify whether the frequency distribution is
correct by analyzing Data Set 12 (POTUS) in Appendix B on page 760 of your textbook.
Years President Lived Class
after First Inauguration Frequency Midpoints
0 –
4
8
5 – 9 2
10 – 14 5
15 – 19 7
20 – 24 4
25 – 29 6
3
0 – 34 0
35 – 39 1
(a) Complete the table with class midpoints.
(b) Calculate the mean number of years a President of the U.S. lived after first inauguration
according to this sample. Round off your answer to two decimal places and use correct
units.
(c) Calculate the standard deviation for this sample. Round off your answer to two decimal
places and use correct units.
(d) Calculate the variance for this sample. Show all work and round off your answer to two
decimal places.
1
2. (1 point) M&M plain candies have a mean weight of 0.8565 g and a standard deviation of
0.0518 g (based on Data Set 20 in Appendix B). The M&M candies used in Data Set 20
came from a package containing 465 candies, and the package label stated that the net weight
is 396.9 g. (If every package has 465 candies, the mean weight of the candies must exceed
396.9/465 = 0.8535 g for the net contents to weigh at least 396.9 g.)
(a) If 1 M&M plain candy is randomly selected, find the probability that it weighs more
than 0.8535 g.
(b) If 465 M&M plain candies are randomly selected, find the probability that their mean
weight is at least 0.8535 g.
3. (1 point) Weights (kg) of poplar trees were obtained from trees planted in a rich and moist
region. The trees were given different treatments identified in the table below. The data are
from a study conducted by researchers at Pennsylvania State University and were provided by
Minitab, Inc. Use a 0.05 significance level to test the claim that the four treatment categories
yield poplar trees with the same mean weight.
No Treatment Fertilizer Irrigation Fertilizer and Irrigation
1.21 0.94 0.07 0.85
0.57 0.87 0.66 1.78
0.56 0.46 0.10 1.47
0.13 0.58 0.82 2.25
1.30 1.03 0.94 1.64
2
4. (1 point) A random sample of stock prices per share (in dollars) is shown. Find the 90%
confidence interval for the variance and standard deviation for the prices. Assume the variable
is normally distributed.
26.69 13.88 28.37 12.00
75.37 7.50 47.50 43.00
3.81 53.81 13.62 45.12
6.94 28.25 28.00 60.50
40.25 10.87 46.12 14.75
5. (1 point) Teens are reported to watch the fewest total hours of television per week of all
the demographic groups. The mean television viewing for teens on Sunday from 1:00 to 7:00
P.M. is 1 hour 13 minutes. A random sample of local teens disclosed the following times
for Sunday afternoon television viewing. At α = 0.01, can it be concluded that the mean is
greater than the national viewing time?
2:30 2:00 1:30 3:20
1:00 2:15 1:50 2:10
1:30 2:30
3
6. (1 point) Listed below are amounts of court fine revenue and salaries paid to the town
justices (based on data from the Poughkeepsie Journal). All amounts are in thousands of
dollars, and all of the towns are in Dutchess County, New York.
Court Income 65 404 1567 1131 272 252 111 154 32
Justice Salary 30 44 92 56 46 61 25 26 18
(a) Is there sufficient evidence to conclude that there is a linear correlation between the
court incomes and justice salaries?
(b) The court of the town of Beekman had income of $83,941. Find the best predicted salary
for the justice.
4
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