Download MULTIPLE CHOICE. Choose the one alternative that best completes

Exam: STAT 2550-056 (Statistics for Science Students), Fall 2016
Practice Test 1
Name___________________________________
Student Number _________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) An industrial supplier has shipped a truckload of teflon lubricant cartridges to an aerospace
customer. The customer has been assured that the mean weight of these cartridges is in excess of
the 12 ounces printed on each cartridge. To check this claim, a sample of n = 15 cartridges are
randomly selected from the shipment and carefully weighed. Summary statistics for the sample
are: x = 12.13 ounces, s = .30 ounce. To determine whether the supplier's claim is true, consider the
test, H0 : µ = 12 vs. Ha : µ > 12, where µ is the true mean weight of the cartridges. Find the rejection
region for the test using = .01.
A) t > 2.977, where t depends on 14 df
B) z > 2.33
C) t > 2.624, where t depends on 14 df
D) |z| > 2.58
1)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
2) A recipe submitted to a magazine by one of its subscribers states that the mean baking
time for a cheesecake is 55 minutes. A test kitchen preparing the recipe before it is
published in the magazine makes the cheesecake 10 times at different times of the day in
different ovens. The following baking times (in minutes) are observed.
54
55
58
59
59
60
61
61
62
2)
65
Assume that the baking times belong to a normal population. Test the null hypothesis that
the mean baking time is 55 minutes against the alternative hypothesis µ > 55. Use = .05.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
3) An industrial supplier has shipped a truckload of teflon lubricant cartridges to an aerospace
customer. The customer has been assured that the mean weight of these cartridges is in excess of
the 11 ounces printed on each cartridge. To check this claim, a sample of n = 23 cartridges are
randomly selected from the shipment and carefully weighed. Summary statistics for the sample
are: x = 11.14 ounces, s = .23 ounce. To determine whether the supplier's claim is true, consider the
test, H0 : µ = 11 vs. Ha : µ > 11, where µ is the true mean weight of the cartridges. Calculate the
value of the test statistic.
A) 1.400
B) 0.609
C) 2.919
D) 14.000
4) 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 87 who indicate that they recommend
this cough syrup. The test statistic in this problem is approximately:
A) -0.66
B) 1.00
C) -1.00
D) -0.50
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3)
4)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
5) State University uses thousands of fluorescent light bulbs each year. The brand of bulb it
currently uses has a mean life of 600 hours. A competitor claims that its bulbs, which cost
the same as the brand the university currently uses, have a mean life of more than 600
hours. The university has decided to purchase the new brand if, when tested, the evidence
supports the manufacturer's claim at the .05 significance level. Suppose 100 bulbs were
tested with the following results: x = 627.5 hours, s = 100 hours. Conduct the test using
= .05.
5)
6) In order to compare the means of two populations, independent random samples of 144
observations are selected from each population with the following results.
6)
Sample 1
Sample 2
x 1 = 7,123
x 2 = 6,957
s1 = 175
s2 = 225
Use a 95% confidence interval to estimate the difference between the population means
(µ1 - µ2 ). Interpret the confidence interval.
7) In order to compare the means of two populations, independent random samples of 225
observations are selected from each population with the following results.
Sample 1
Sample 2
x 1 = 478
x 2 = 481
s1 = 14.2
7)
s2 = 11.2
Test the null hypothesis H0 : (µ1 - µ2 ) = 0 against the alternative hypothesis
Ha : (µ1 - µ2 )
0 using
= .10. Give the significance level, and interpret the result.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
8) The business college computing center wants to determine the proportion of business students
who have laptop computers. If the proportion differs from 30%, then the lab will modify a
proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic
is 2.5. Find the p-value for a two-tailed test of hypothesis.
A) .0124
B) .4938
C) .4876
D) .0062
8)
9) A marketing study was conducted to compare the mean age of male and female purchasers of a
certain product. Random and independent samples were selected for both male and female
purchasers of the product. It was desired to test to determine if the mean age of all female
purchasers exceeds the mean age of all male purchasers. The sample data is shown here:
9)
Female: n = 20,
Male:
n = 20,
sample mean = 50.30,
sample mean = 39.80,
sample standard deviation = 13.215
sample standard deviation = 10.040
Use the pooled estimate of the population standard deviation to calculate the value of the test
statistic to use in this test of hypothesis.
A) t = 2.17
B) t = 2.65
C) t = 3.17
D) t = 2.83
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10) When blood levels are low at an area hospital, a call goes out to local residents to give blood. The
blood center is interested in determining which sex - males or females - is more likely to respond.
Random, independent samples of 60 females and 100 males were each asked if they would be
willing to give blood when called by a local hospital. A success is defined as a person who
responds to the call and donates blood. The goal is to compare the percentage of the successes of
the male and female responses. Suppose 45 of the females and 60 of the males responded that they
were able to give blood. Find the test statistic that would be used if it is desired to test to determine
if a difference exists between the proportion of the females and males who responds to the call to
donate blood.
A) z = 2.01
B) z = 1.93
C) z = 1.96
D) z = 1.645
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10)
Answer Key
Testname: SAMPLE1
1) C
2) x = 59.4, s = 3.24; The test statistic is t =
59.4 - 55
3.24 / 10
4.29. The rejection region is t > 1.833. Since the test statistic falls in
the rejection region, we reject the null hypothesis in favor of the alternative hypothesis. We conclude that the true
mean baking time is actually greater than 55 minutes.
3) C
4) C
5) To determine if the mean life exceeds 600 hours, we test:
H0 : µ = 600 vs. Ha : µ > 600
The test statistic is z =
x - µ0
x - µ0
/ n
s/ n
=
627.5 - 600
= 2.75.
100/ 100
Since the test is greater than 1.645, H0 can be rejected. There is sufficient evidence to indicate the average life of the
new bulbs exceeds 600 hours when testing at = .05.
1752 2252
166 ± 46.56
+
6) (7,123 - 6,957) ± 1.96
144
144
7) The test statistic is z =
478 - 481
14.12 11.22
+
225
225
-2.50
8) A
9) D
10) B
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