ST 311 Final: ST 311 NCSU Final Exam 311 601
ST 311 ReilandPRACTICE PROBLEMS FOR FINAL EXAM
Topics covered on final exam : Chapters 20, 21, 22.5-22.6, 23-25 in text.
This material is covered in webassign homework assignments 9 through 12
Exam information: 3 hour time limit; materials allowed: calculator (no laptops or tablets),
1 8 x11 sheet of paper (2 sided)with notes, definitions, formulas, etc. Normal table, t-table, and chi-
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square table will be provided with the exam.
Questions on the final exam will be both multiple choice and numerical answerImportant Note:
format.
Answers are at the end of the document.
Practice Problems
1. (confidence interval for mean ) In a on fires in compartmented fire-resistant.Risk Management Study
buildings, the data below was generated. The data in the table give the number of victims who died
trying to evacuate for a sample of 14 recent fires.
NUMBER OF
FIRE VICTIMS
Las Vegas Hilton (Las Vegas) 5
Inn on the Park (Toronto) 5
Westchase Hilton (Houston) 8
Holiday Inn (Cambridge, Ohio) 10
Conrad Hilton (Chicago) 4
Providence College (Providence) 8
Baptist Towers (Atlanta) 7
Howard Johnson (New Orleans) 5
Cornell University (Ithaca) 9
Westport Central Apartments (Kansias City, MO) 4
Orrington Hotel (Evanston IL) 0
Hartford Hospital (Hartford, CT) 16
Milford Plaza (New York) 0
MGM Grand (Las Vegas) 36
Source: Macdonald, J. N. “Is Evacuation a Fatal Flaw in Fire-Fighting Philosophy?”
Vol. 33, No. 2, Feb. 1986, p. 37Risk Management,
a. State the assumption, in terms of the problem, that is required for the confidence interval
technique to be valid.
b. Construct a 98% confidence interval for the true mean number of victims per fire who die
attempting to evacuate compartmented fire-resistant buildings.
c. Interpret the interval constructed in part b.
2. (confidence interval for the difference between means) To investigate the possible link..
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between fluoride content of drinking water and cancer, the cancer death rates (number of deaths per
100,000 population) from 1952-1969 in 20 selected U. S. cities - the ten largest fluoridated cities and
the ten largest cities not fluoridated by 1969 - were recorded. These data were used to calculate for
each city the annual rate of increase in cancer death rate over this 18 year period. The data are given
below:
ST 311 Final Exam Practice Problems page 2
FLUORIDATED NONFLUORIDATED
Annual Increase in Annual Increase in
City Cancer Death Rate City Cancer Death Rate
Chicago 1.0640 Los Angeles .8875
Philadelphia 1.4118 Boston 1.7358
Baltimore 2.1115 New Orleans 1.0165
Cleveland 1.9401 Seattle .4923
Washington 3.8772 Cincinnati 4.0155
Milwaukee -.4561 Atlanta -1.1744
St. Louis 4.8359 Kansas City 2.8132
San Francisco 1.8875 Columbus 1.7451
Pittsburgh 4.4964 Newark -.5676
Buffalo 1.4045 Portland 2.4471
a. Construct a 95% confidence interval for the difference between the mean annual increases in
cancer death rates for fluoridated and nonfluoridated cities. (Use 18 degrees of freedom; do not
assume equal variances).
b. What assumption(s) must be satisfied for the confidence interval in part a) to be valid?
3. (hypothesis test for ) Domino's Pizza in Big Rapids, Michigan, advertises that they deliver your pizza.
within 15 minutes of placing an order or it is free. A sample of 25 customers is selected at random.
The average delivery time in the sample was 13 minutes with a sample standard deviation of 4
minutes.
a. Test to determine if we can infer at the 5% significance level that the population mean is less than
15 minutes.
b. What is the required condition of the technique used in part (a)?
c. Approximate the P-value for this test.
4. (confidence interval for mean ) A marketing consultant was interested in estimating the mean weekly.
consumption of soft drinks among teenagers. A random sample of teenagers were asked how many'"
ounces of soft drink they consume daily. The sample mean and sample standard deviation are,
respectively, 22.38 and 5.17. Estimate with 99% confidence the mean daily consumption of soft
drinks by teenagers.
5. (linear regression) A simple linear regression was used to predict the score on a final exam from they
score on the first exam. The slope of the least squares regression line is .75. The standard error ofx
the slope is .11 and the sample size is 200. A 90% confidence interval for the true slope is (though the
.0 8 # .0 > is , use 200 in the -table)
a. .64 to .86 b. .53 to .97 c. .57 to .93 d. .64 to .86 e. none of the above
6. (linear regression) Refer to the previous problem. To test the null hypothesis that the slope is zero
versus the one-sided alternative that the slope is positive, we use the test statistic tœ
a. 6.82 b. .05 c. .15 d. .95 e. .75
7. (chi-square test) When two competing teams are equally matched, the probability that each team wins
any game is 0.5. The (NBA) championship goes to the team thatNational Basketball Association
wins four games in a best-of-seven series. If the teams were evenly matched, the probability that the
final series ends with one of the teams sweeping four straight games would be 2(0.5) = 0.125 [team
%
A wins in 4 games with probability (0.5) team B can also win in 4 games with the same probability,
%à
so the probability the series ends in 4 games is 2(0.5) ].
%
Similarly team A can win in 5 games if team A wins 3 of the first 4 games and then wins game 5. So
team A wins in 5 games with probability . But team B can also win in
%$ $
G Ð!Þ&Ñ Ð!Þ&чÐ!Þ&Ñ œ !Þ"#&
5 games with the same probability, so the probability that the series ends in 5 games is . Similar!Þ#&
ST 311 Final Exam Practice Problems page 3
probability calculations show that the probability is that the series lasts six games, and the!Þ$"#&
probability is that the series lasts the full seven games. The table below shows the number of!Þ$"#&
games it took to decide each of the last 57 NBA champs. Do you think the teams are usually equally
matched? Give statistical evidence to support your conclusion.
Length of series 4 games 5 games 6 games 7 games
NBA finals 7 13 22 15
8. (chi-square test for homogeneity) The president of a large university has been studying the
relationship between male/female supervisory structures in his institution and the level of employees'
job satisfaction. The results of a recent survey are shown in the table below. Conduct a test at the
5% significance level to determine whether the level of job satisfaction depends on the
boss/employee gender relationship.
Male/Female Female/Male Male/Male Female/Female
Satisfied 60 15 50 15
Neutral 27 45 48 50
Dissatsfied 13 32 12
Boss/Employee
Level of Satisfaction
55
9. (P-value) (True or false) In a hypothesis test, a P-value of 0.03 means that there is only probability
0.03 that the null hypothesis is true.
10. (hypothesis test for ) Suppose that 9 observations are drawn from a population whose distribution.
can be described by a normal model. The observations are:
15 9 13 11 8 12 11 7 10
Note that and You want to test whether the mean of the population from whichB œ "!Þ'( = œ #Þ&Þ
this sample was taken is different from 12.
a. State the null and alternative hypotheses.
b. Compute the value of the test statistic.
c. Approximate the P-value.
d. What is your conclusion?
11. (linear regression) Sociologists are of the opinion that there has been a decrease in the difference in
ages at first marriage for men and women since 1975. We want to examine data to determine if this
decrease is significant. The following data summary and regression results were obtained, where the B
variable is year and the variable is the age difference (husband age wife age) at first marriage.C
Variable Count Mean StDev
Year ( ) 24 1986.5 7.071B
husband-wife age ( ) 24 2.3125 0.249C
