Download Hypothesis Testing Quiz - Chapter 10

AP Stats Mr. Honberger
Review Ch. 9 and 10
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Date_________Per________
1. Assume that a computer was used to generate the given confidence interval for the population mean,
 . Find the sample mean or margin of
error as specified. (145, 157). Find the sample mean, x .
a) 151.0
b) 150.5
c) 145
d) 152.5
Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.
2. Carter Motor Company claims that its new sedan, the Libra, will average better than 28 miles/gallon in the city. Identify the type I error for the
test.
a) The error of rejecting the claim that the mean is at most 28 mpg when it really is at most 28 mpg.
b) The error of failing to reject the claim that the mean is at most 28 mpg when it is actually greater than 28 mpg.
c) The error of rejecting the claim that the true proportion is more than 28 mpg when it really is more than 28 mpg.
3. An Entomologist writes an article in a scientific journal which claims that fewer than 11 in ten thousand male fireflies are unable to produce
light due to a genetic mutation. Identify the type I error for the test.
a) The error of rejecting the claim that the true proportion is at least 11 in ten thousand when it really is less than 11 in ten thousand.
b) The error of failing to reject the claim that the true proportion is at least 11 in ten thousand when it is actually less than 11 in ten thousand.
c) The error of rejecting the claim that the true proportion is at least 11 in ten thousand when it really is at least 11 in ten thousand.
4. A researcher claims that 62% of voters favor gun control. Identify the type II error for the test.
a) The error of rejecting the claim that the proportion favoring gun control is more than 62% when it really is more than 62%.
b) The error of failing to reject the claim that the proportion favoring gun control is 62% when it is actually different than 62%.
c) The error of rejecting the claim that the proportion favoring gun control is 62% when it really is less than 62%.
Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null
hypothesis.
5.
 = 0.03 for a two-tailed test.
a) ± 1.953
b) ± 2.33
c) ± 2.17
d) ± 2.052
6.
 = 0.07; H1 is  > 62.4
a) 1.48
b) ± 1.81
c) -1.48
d) 1.81
Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that
would result in rejection of the null hypothesis.
7. Suppose you wish to test the claim that  > 10. Given the sample of n=50 and a significance level of
for rejecting the null hypothesis?
a) Reject Ho if test statistic > 1.28
c) Reject Ho if test statistic > 1.645 or < -1.645
 = 0.10, what criterion would be used
b) Reject Ho if test statistic < 1.28
d) Reject Ho if test statistic > 1.645
8. A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 130 of
the school’s students, 32% of them plan to go into general practice. Find the P-value for a test of the school’s claim.
a) 0.1635
b) 0.3078
c) 0.1539 d)
0.3461
Find the minimum sample size you should use to assure that your estimate,
p , will be within the required margin of error around p.
9. A survey of shoppers is planned to see what percentage use credit cards. Prior to surveys suggest 65% of shoppers use credit cards. The
required margin of error is 0.04. The confidence level is 95%.
a) 491
b) 546
c) 942
d) 1561
Identify the null hypothesis Ho and the alternative hypothesis H1. Use  for a claim about a mean, p for a claim about a proportion, and  for a
claim about variation.
10. An entomologist writes an article in a scientific journal which claims that fewer than 16 in ten thousand male fireflies are unable to produce
light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light.
a) HO: p> 0.0016
H1: p< 0.0016
b) HO: p> 0.0016 c) HO: p<0.0016
H1: p< 0.0016
H1: p> 0.0016
d) HO: p < 0.0016
H1: p > 0.0016
11. A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 5 in every one thousand.
a) HO: p< 0.005
H1: p>0.005
b) HO: p> 0.005
H1: p< 0.005
c) HO: p>0.005
H1: p< 0.005
d) HO: p < 0.005
H1: p > 0.005
12. A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the σ = 3.3
mg claimed by the manufacturer.
a) HO: σ < 3.3 mg
H1: σ > 3.3 mg
b) HO: σ  3.3 mg c) HO: σ > 3.3 mg d) HO: σ = 3.3 mg
H1: σ = 3.3 mg
H1: σ < 3.3 mg
H1: σ  3.3 mg
13. A 99% confidence interval (in inches) for the mean height of a population is 65.5 < µ < 66.9. This result is based on a sample size of 144.
Construct the 95% confidence interval. (Hint: you will first need to find the sample mean and sample standard deviation.)
a) 65.3 in < µ < 67.1 in
b) 65.6 in < µ < 66.8 in
c) 65.5 in < µ < 66.9 in
d) 65.7 in < µ < 66.7 in
14. True or false: In a hypothesis test, an increase in  will cause a decrease in the power of the test provided the sample size is kept fixed.
a) True
b) False
15. A pollster wishes to estimate the true proportion of U.S. voters that oppose capital punishment. How many voters should be surveyed in order
to be 95% confident that the true proportion is estimated to within 0.04?
a) 601
b) 25
c )1
d) 600
16. True or false: In a hypothesis test regarding a population mean, the probability of a type II error, ß, depends on the true value of the
population mean.
a) True
b) False
17. In a hypothesis test, which of the following will cause a decrease in ß, the probability of making a type II error?
A: Increasing  while keeping the sample size n, fixed
B: Increasing the sample size n, while keeping  fixed
C: Decreasing  while keeping the sample size n, fixed
D: Decreasing the sample size n, while keeping  fixed
a) C and D
b) A and B
c) B and C
d) A and D
18. Suppose the federal government needs to estimate the proportion of students receiving federal loans that default on those loans. How many
past records on student loans should be examined in order to be 97% confident that the true proportion is estimated to within 0.006?
a) 15,070
b) 523,212
c) 130,803
d) 32,701
19. In a hypothesis test, the null hypothesis of  < 81 is rejected because the P-value was less than 0.05. The sample size was 55 and the sample
mean was 84.5. What is the largest possible value of the standard deviation?
a) 20.28
b) 13.24
c) 2.12
d) 15.73
20. The following confidence interval is obtained for a population proportion, p: (0.399, 0.437)
Use these confidence interval limits to find the point estimate, p .
a) 0.423
b) 0.399
c) 0.437
d) 0.418
Use the given claim and test statistic to find the P-value.
21. Claim: The mean systolic blood pressure of women aged 40-50 in the U.S. is equal to 126 mmHg.
Test statistic: z = 1.72
a) 0.9146
b) 0.0854
c) 0.0472
d) 0.9573
22. Claim: The mean monthly salary of employees at one company is at most $32,500.
Test statistic: z = 0.52
a) 0.3015
b) 0.6985
c) 0.6030
d) 0.3970
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
23. n=137, x=69, 90%
a) (0.436, 0.572)
b) (0.437, 0.571)
c) (0.434, 0.574)
d) (0.432, 0.576)
Use the given degree of confidence and sample data to construct a confidence interval for the population mean  .
24. A laboratory tested 80 chicken eggs and found that the mean amount of cholesterol was 213 milligrams with s=12.8 milligrams. Construct a
95% confidence interval for the true mean cholesterol content,  , of all such eggs.
A) (210,216)
b) (209,216)
c) (209, 215)
d) (211,217)
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
25. A survey of 865 voters in one state reveals that 408 favor approval of an issue before legislature. Construct the 95% confidence interval for
the true proportion of all voters in the state who favor approval.
A) 0.471<p<0.472
b) 0.444<p<0.500
c) 0.435<p<0.508
d) 0.438<p<0.505
Use the given degree of confidence and sample data to construct a confidence interval for the population mean  .
26. Test scores n=91,
x
=83.7, s=7.4; 99 percent
a) (81.9,85.5)
b) (82.4) 85.0)
c) (81.7, 85.7)
d) (82.2, 0.85.2)
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
27. n=53, x=15; 95 percent
a) (0.18, 0.386)
b) (0.161, 0.405)
c) (0.162, 0.404)
d) (0.181, 0.385)
Free Response problems.
28. The national weather service says that the mean daily high temperature for October in a large Midwestern city is 56°F. A local
weather service wants to test the claim of 56°F because it believes it is lower. A sample of mean daily high temperatures for October over the
past 31 years yields x =54°F and s=5.6°F. Test the claim at a=0.01 significance level.
29. A newspaper in a large Midwestern city reported that the National Association of Realtors said that the mean home price last year was
$116,800. The city housing department feels that this figure is too low. They randomly selected 66 home sales with x=118,900 and a standard
deviation of s=$3,700. Use a 5% level significance to test the $116,800 figure.
30. The Maine Department of National Resources reported that the mean weight of lobsters trapped in the state is 1.7 pounds. Carl Lewis is a
lobster trapper off the coast of Maine. Carl suspects this figure is too high so he records the weights of a random sample of 45 lobsters that he
trapped. If x=1.5 pounds and s=0.6 pounds, use a 1 percent level of significance to test the state’s figures of 1.7 pounds.
31. Suppose that you perform a hypothesis test regarding a population mean, and that the evidence does not warrant rejection of the null
hypothesis. When formulating the conclusion to the test, why is the phrase “fail to reject the null hypothesis” more accurate than the phrase
“accept the null hypothesis”?
32. A department store accepts only its own credit card. Among 36 randomly selected card holders, it was found that the mean amount owed was
$175.37, while the standard deviation was 84.77. Using a significance level of 0.05, test the claim that the mean amount owed by all
customers is greater than $150.00
33. According to a recent poll 53% of Americans would vote for the incumbent president. If a random sample of 100 people results in 45% who
would vote for the incumbent, test the claim that the actual percentage is 53%. Use a 0.10 significance level.
34. In a clinical study of an allergy drug, 108 of the 203 subjects reported experiencing significant relief from their symptoms. At the 0.01
significance level, test the claim that more than half of all those using the drug experience relief.
35) A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect
rate is 5.9% but the manager claims that this is only a sample fluctuation and production is not really out of control. At the 0.01 level of
significance, test the manager’s claim.
Answers:
1) A
15) A
2) A
16) A
3) C
17) B
4) B
18) D
5) C
19) D
6) A
20) D
7) A
21) B
8) C
22) A
9) B
23) C
10) A
24) A
11) C
25) D
12) D
26) C
13) B
27) C
14) B
28) H 0 :   56 H A :   56 t  1.99 Pvalue  .028 Fail to Reject H 0
I can not say with 99 % confidence that the true mean temp is less than 56 F.
29) H 0 :   116800 H A :   116800 t  4.61 Pvalue  0 Reject H 0
I can say with 95 % confidence that the true mean home price is higher than $116,800.
30) H 0 :   1.7 H A :   1.7 t  2.24 Pvalue  .015 Fail to Reject H 0
I can not say with 99 % confidence that the true mean lobster weight is lower than 1.7 pounds.
31) In a hypothesis test, we do not prove the null hypothesis; we just determine whether we have sufficient evidence to reject the null
hypothesis. If there is not sufficient evidence, this does not necessarily imply that the null hypothesis is true but that we don’t have
enough evidence to reject it.
32) H 0 :   150 H A :   150 t  1.8 Pvalue=.04 Reject H 0
I can say with 95 % confidence that the true mean amount owed by all credit card customers is larger than $150.
33) H 0 : p  .53 H A : p  .53 z  1.6 Pvalue  .11 Fail to Reject H 0
I can not say with 90 % confidence that the true proportion of voters who would vote for the incumbent is not equal to 53%.
34) H 0 : p  .5 H A : p  .5 z  .91 Pvalue  .18 Fail to Reject H 0
I can not say with 99 % confidence that the true proportion of subjects who reported experiencing significant relief from
their symptoms is greater than .5
35) H 0 : p  0.03 H A : p  0.03 z  1.56 Pvalue  .059 Fail to Reject H 0
I can not say with 99 % confidence that the true defect rate is more than 3%