# Statistics Homework

MATH 16 Elementary Statistics Monterey Peninsula College

Student Name Date Score

Final Exam – Part #1 Chapters 1 through 10, 12: 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

30 - 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.

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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

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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

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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.

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