ST 311 Final: ST 311 NCSU problems Final Exam 311
ST 311 Reiland PRACTICE PROBLEMS FOR FINAL EXAM
Topics covered on final exam : Chapters 19-27 in text.
This material is covered in webassign homework assignments 9 through 12
Exam information: 3 hour time limit; materials allowed: calculator (no laptops), 1 8 x11 sheet
"
#
of paper (2 sided)with notes, definitions, formulas, etc. Normal, t, and chi-square tables will be
provided with the exam.
The questions on the final exam will be multiple choice format.
Answers are at the end of the document.
1. (True or false) In a test of significance, a P-value of 0.03 means that there is only probability 0.03 that
the null hypothesis is true.
2. In a on fires in compartmented fire-resistant buildings, the data below wasRisk Management Study
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, 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.
3. A -value is the probability: T
a. of committing a Type I error
b. of committing a Type II error
c. calculated assuming is true, that the test statistic would assume a value as or more extremeL!
than the value stated in the null hypothesis
d. calculated assuming is true, that the test statistic would assume a value as or more extremeL!
than the observed value of the test statistic.
e. that is true.L!
ST 311 Final Exam Practice Problems page 2
f. that we have made a mistake, assuming is trueL!
4. Which of the following statements is false?
a. The t distribution is symmetric about zero
b. The t distribution is more spread out than the standard normal distribution
c. As the degrees of freedom get smaller, the t-distribution's dispersion gets smaller
d. The t distribution is mound-shaped
5. The Student t distribution approaches the normal distribution as the:
a. degrees of freedom increase
b. degrees of freedom decrease
c. sample size decreases
d. population size increases
6. The statistic has the student t distribution if the sample is selected from:
B.
=
8
a. a population that can be described by a Student t model
b. a population that can be described by a normal model
c. a negatively skewed distribution (skewed to the left)
d. a positively skewed distribution (skewed to the right)
7. 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 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 the population mean is less than 15 minutes.
b. What is the required condition of the technique used in part (a)?
c. Approximate the -value for this test.T
8. 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 sum of the observations and the sum of the squared observations are shown below.
1 and
3œ" 3œ"
'" '"
33
#
B œ $'& ÐB BÑ œ "'!&Þ$#)
Estimate with 99% confidence the mean daily consumption of soft drinks by teenagers.
9. Suppose that 9 observations are drawn from a population that is approximately symmetric and mound-
shaped. The observations are:
15 9 13 11 8 12 11 7 10
You want to test whether the mean of the population from which this sample was taken is different
from 10.
a. State the null and alternative hypotheses.
b. Compute the value of the test statistic.
c. Compute the -value.T
10. As the sample size n increases, when the confidence level is held fixed the width of the confidence
interval for the population mean tends to :
a. increase
b. decrease
c. stay the same
ST 311 Final Exam Practice Problems page 3
11. A random sample of size 49 was selected; the resulting sample standard deviation . Suppose= œ ( )#*
the confidence interval formed for was 63 < < 69...
a. What is the sample mean, ?B
b. What is the standard error of ?B
c. What was the confidence coefficient used to form the confidence interval?
12. A confidence coefficient of 0.99 can correctly be interpreted to mean that
a. 99% of the time in repeated sampling, intervals using an appropriate formula will contain
the sample value.
b. 99% of the time in repeated sampling, intervals using an appropriate formula will contain
the relevant population parameter.
c. 99% of the time in repeated sampling, intervals using an appropriate formula will contain
the sample value as the midpoint of the interval.
d. 99% of the time in repeated sampling, intervals using an appropriate formula will contain
the sample mean as their midpoints.
13. Perform the hypothesis test shown below,
LÀ:œÞ!&
!
LÀ:Þ!&
+
given that a random sample of size 1000 revealed that the number of successes was 40. Compute
the P-value and use it to make a conclusion concerning the hypothesis test.
14. A professor claims that 70% of College of Business graduates earn more than $45,000 per year. In a
random sample of 300 graduates, 195 earn more than $45,000. Perform a hypothesis test to evaluate
the professor's claim.
15. To test the hypotheses
LÀ:œÞ!'
!
,LÀ:Þ!'
+
a random sample of size 1000 revealed that the number of successes was 40. Compute the -valueT
and explain how to use it to test the hypothesis.
16. A candy company claims that in a large bag of St. Patrick's Day candy half the candies are green and
half are white. You select candies at random from a bag and discover that of the first 50 you eat, only
15 are green. This makes you suspicious of the company's claim that half are green and half are white.
Perform a hypothesis test to test the company's claim.
17. In the 1980's it was generally believed that congenital abnormalities affected about 5% of the nation's
children. Some people believe that the increase in the number of chemicals in the environment has
lead to an increase in the incidence of abnormalities. A recent study examined 408 children and found
that 48 of them showed signs of an abnormality. Is this evidence that the risk has increased?
i) Let denote the proportion of children with genetic abnormalities. Choose the correct null and:
alternative hypotheses.
A. vs B. vs L À : œ !Þ""(' L À : !Þ""('à L À : œ Þ!& L À : Þ!&
ss
!!
EE
C. vs D. vs L À : œ Þ!& L À : Á Þ!&à L À : œ Þ!& L À : Þ!&
!!
EE
E. vs F. vs L À : œ Þ!& L À : Þ!& L À : œ !Þ""(' L À : Á !Þ""('
ss
!!
EE
ii) What is the value of the test statistic?
iii) What is the ?P-value
iv) What is your conclusion?
18. Recently there have been campaigns encouraging people to save energy by carpooling to work.
Some cities have created “carpool only" traffic lanes (i. e. only cars with 2 or more passengers can
use these lanes). In order to evaluate the effectiveness of carpool only lanes, toll booth personnel in
one city monitor 2,000 randomly selected cars in 2005 before the carpool lanes were established and
