Download Quiz 7

STT 315 Lecture 3
04/17/2014
Quiz 7 (Chapter 7)
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Directions: The quiz contains 16 multiple choice questions. Each question will be worth 1 point so that total points for this quiz is 16.
There is only one correct answer per question. If you would like to get partial credit, show your work below the question where it is
appropriate. The formulas which may be needed for the quiz are given below.
1) A small private college is interested in determining the percentage of its students who live off
campus and drive to class. Specifically, it was desired to determine if less than 20% of their current
students live off campus and drive to class. Suppose a sample of 108 students produced a test
statistic of z = -1.35. Find the p-value for the test of interest to the college.
A) p = 0.4115
B) p = 0.9115
C) p = 0.1770
D) p = 0.0885
1)
Work:
2) I want to test H0 : p = .7 vs. Ha : p ≠ .7 using a test of hypothesis. This test would be called a(n)
____________ test.
A) two-tailed
B) upper-tailed
C) lower-tailed
2)
D) one-tailed
3) Consider a test of H0 : μ = 9. For the following case, give the rejection region for the test in terms of
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the z-statistic: Ha : μ < 9, α = 0.01
A) z > -2.33
B) z < 2.575
C) z < -2.575
D) z < -2.33
4) A consumer product magazine recently ran a story concerning the increasing prices of digital
cameras. The story stated that digital camera prices dipped a couple of years ago, but now are
beginning to increase in price because of added features. According to the story, the average price
of all digital cameras a couple of years ago was $215.00. A random sample of n = 22 cameras was
recently taken and entered into a spreadsheet. It was desired to test to determine if that average
price of all digital cameras is now more than $215.00. Find a rejection region appropriate for this
test if we are using α = 0.05.
A) Reject H0 if t > 2.080 or t < -2.080
B) Reject H0 if t > 1.717
C) Reject H0 if t > 1.725
4)
D) Reject H0 if t > 1.721
5) A company claims that 9 out of 10 doctors (i.e., 90%) recommend its brand of cough syrup to their
patients. To test this claim against the alternative that the actual proportion is less than 90%, a
random sample of doctors was taken. Suppose the test statistic is z = -2.23. Can we conclude that
H0 should be rejected at the a) α = .10, b) α = .05, and c) α = .01 level?
A) a) yes; b) yes; c) no
C) a) no; b) no; c) no
B) a) no; b) no; c) yes
D) a) yes; b) yes; c) yes
Work:
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5)
6) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The
owner of the store has determined that home delivery will be successful only if the average time
spent on a delivery does not exceed 36 minutes. The owner has randomly selected 21 customers
and delivered pizzas to their homes in order to test whether the mean delivery time actually
exceeds 36 minutes. What assumption is necessary for this test to be valid?
A) The population variance must equal the population mean.
B) The population of delivery times must have a normal distribution.
C) None. The Central Limit Theorem makes any assumptions unnecessary.
D) The sample mean delivery time must equal the population mean delivery time.
6)
7) The owner of Get-A-Away Travel has recently surveyed a random sample of 183 customers to
determine whether the mean age of the agency's customers is over 32. The appropriate hypotheses
are H0 : μ = 32, Ha : μ > 32. If he concludes the mean age is over 32 when it is not, he makes a
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__________ error. If he concludes the mean age is not over 32 when it is, he makes a __________
error.
A) Type I; Type II
B) Type II; Type I
C) Type I; Type I
D) Type II; Type II
8) A bottling company produces bottles that hold 12 ounces of liquid. Periodically, the company gets
complaints that their bottles are not holding enough liquid. To test this claim, the bottling company
randomly samples 25 bottles and finds the average amount of liquid held by the bottles is 11.8
ounces with a standard deviation of .4 ounce. Which of the following is the set of hypotheses the
company wishes to test?
A) H0 : μ < 12 vs. Ha : μ = 12
B) H0 : μ = 12 vs. Ha : μ > 12
C) H0 : μ = 12 vs. Ha : μ ≠ 12
8)
D) H0 : μ = 12 vs. Ha : μ < 12
9) The business college computing center wants to determine the proportion of business students who
have laptop computers. If the proportion differs from 25%, then the lab will modify a proposed
enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is 2.4. Find
the p-value for a two-tailed test of hypothesis.
A) .4918
B) .0082
C) .0164
D) .4836
9)
Work:
10) A company claims that 9 out of 10 doctors (i.e., 90%) recommend its brand of cough syrup to their
patients. To test this claim against the alternative that the actual proportion is less than 90%, a
random sample of 100 doctors was chosen which resulted in 94 who indicate that they recommend
this cough syrup. The test statistic in this problem is approximately:
A) 1.33
B) 1.83
C) -1.33
D) 1.67
10)
Work:
11) A bottling company produces bottles that hold 12 ounces of liquid. Periodically, the company gets
complaints that their bottles are not holding enough liquid. To test this claim, the bottling company
randomly samples 64 bottles and finds the average amount of liquid held by the bottles is 11.9155
ounces with a standard deviation of 0.40 ounce. Suppose the p-value of this test is 0.0655. State the
proper conclusion.
A) At α = 0.025, reject the null hypothesis.
B) At α = 0.05, fail to reject the null hypothesis.
C) At α = 0.05, accept the null hypothesis.
D) At α = 0.05, reject the null hypothesis.
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11)
12) How many tissues should a package of tissues contain? Researchers have determined that a person
uses an average of 61 tissues during a cold. Suppose a random sample of 2500 people yielded the
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following data on the number of tissues used during a cold: x = 51, s = 25. Suppose the
corresponding test statistic falls in the rejection region at α = .05. What is the correct conclusion?
A) At α = .05, accept Ha .
B) At α = .10, reject Ha .
C) At α = .10, reject H0 .
D) At α = .05, reject H0 .
Work:
13) Which of the following cases do have the sample size which is large enough to use the normal
approximation methodology to conduct a test of the null hypothesis H0 :p=p0.
A) n=1100, p0 = 0.99
B) n=65, p0 = 0.8
C) n=600, p0 = 0.01
D) n=80, p0 = 0.4
13)
Work:
14) One-Sample T Test
Null Hypothesis: μ = 215
Alternative Hyp: μ > 215
Variable
Camera Price
14)
95% Conf Interval
Mean
SE
Lower
Upper
245.23 15.620 212.740 277.720 1.94
21
T
DF
0.0333
P
Cases Included 22
Is a sample size n = 22 large enough to utilize the central limit theorem in this inferential
procedure?
A) Yes, since the central limit theorem works whenever means are used
B) Yes, since both np and nq are greater than or equal to 15
C) No, since either np or nq is less than 15
D) No, since n < 30
15) A bottling company produces bottles that hold 10 ounces of liquid. Periodically, the company gets
complaints that their bottles are not holding enough liquid. To test this claim, the bottling company
randomly samples 22 bottles and finds the average amount of liquid held by the bottles is 9.7
ounces with a standard deviation of .4 ounce. Calculate the appropriate test statistic.
A) z=-3.437
B) t=-2.225
C) z=-16.500
D) t=-3.518
15)
Work:
16) A significance level for a hypothesis test is given as α = .01. Interpret this value.
A) The probability of making a Type I error is .01.
B) The smallest value of α that you can use and still reject H0 is .01.
C) There is a 1% chance that the sample will be biased.
D) The probability of making a Type II error is .99.
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16)
Answer Key
Testname: STT315_QUIZ 7_SOLUTIONS
1) D
2) A
3) D
4) D
5) A
6) B
7) A
8) D
9) C
10) A
11) B
12) D
13) D
14) D
15) D
16) A
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