Deck 10: Hypothesis Tests Regarding a Parameter

Question 1

The mean utility bill in one city during the summer was less than $90. Write the null and alternativehypotheses.

Answer 1

Question 2

True or False: If I specify β to be equal to 0.36, then the value of α must be 0.64.

Answer 2

False

Question 3

The ______________ hypothesis contains the ʺ=ʺ sign.

A) null
B) alternative
C) explanatory
D) conditional

Answer 3

A

Question 4

The mean age of judges in Los Angeles is 48.6 years. Identify the type I and type II errors for the hypothesis testof this claim.

Question 5

The mean age of lawyers in New York is 50.7 years. Write the null and alternative hypotheses.

Question 6

The mean monthly cell phone bill for one household was less than $93. Identify the type I and type II errors forthe hypothesis test of this claim.

Question 7

The mean repair bill of cars is greater than $110. Write the null and alternative hypotheses.

Question 8

What is the probability associated with not making a Type II error?

Question 9

A hypothesis test is a ʺtwo-tailedʺ if the alternative hypothesis contains a _______ sign. 2 Explain Type I and Type II errors.

Question 10

A) Left-tailed,
B) Right-tailed,
C) Right-tailed,
D) Left-tailed,

Question 11

The owner of an outdoor store recommends against buying the new model of one brand of GPS receiversbecause they vary more than the old model, which had a standard deviation of 50 meters. Write the null andalternative hypotheses.

Question 12

A referendum for an upcoming election is favored by more than half of the voters. Identify the type I and typeII errors for the hypothesis test of this claim.

Question 13

A popular referendum on the ballot is favored by more than half of the voters. Write the null and alternativehypotheses.

Question 14

A local tennis pro-shop strings tennis rackets at the tension (pounds per square inch) requested by thecustomer. Recently a customer made a claim that the pro-shop consistently strings rackets at lower tensions, onaverage, than requested. To support this claim, the customer asked the pro shop to string 12 new rackets at 53psi. Upon receiving the rackets, the customer measured the tension of each and calculated the followingsummary statistics: psi. In order to conduct the test, the customer selected a significance levelof α = .05. Interpret this value.

A) The probability of concluding that the true mean is less than 53 psi when in fact it is equal to 53 psi is only .05.
B) The smallest value of α that you can use and still reject H0 is 0.05.
C) The probability of making a Type II error is 0.95.
D) There is a 5% chance that the sample will be biased.

Question 15

The mean cost of textbooks for one class is greater than $140. Identify the type I and type II errors for thehypothesis test of this claim.

Question 16

The mean annual return for an employeeʹs IRA is at most 4.7 percent. Write the null and alternativehypotheses.

Question 17

A) Two-tailed,
B) Two-tailed,
C) Right-tailed,
D) Left-tailed,

Question 18

A) Right-tailed,
B) Left-tailed,
C) Right-tailed,
D) Left-tailed,

Question 19

A ______________ is a statement or claim regarding a characteristic of one or more populations.

A) hypothesis
B) conclusion
C) conjecture
D) fact

Question 20

The mean annual return for an employeeʹs IRA is at most 3.4 percent. Write the null and alternativehypotheses.

Question 21

A candidate for state representative of a certain state claims to be favored by at least half of the voters. If ahypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

Question 22

A candidate for state representative of a certain state claims to be favored by at least half of the voters. If ahypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis? 10.2 Hypothesis Tests for a Population Proportion1 Explain the logic of hypothesis testing.

Question 23

The mean age of judges in Dallas is greater than 50.2 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

A) There is not sufficient evidence to support the claim
B) There is sufficient evidence to reject the claim
C) There is not sufficient evidence to reject the claim
D) There is sufficient evidence to support the claim

Question 24

Suppose you want to test the claim that Given a sample size of n=48 and a level of significance of =0.01 , when should you reject H₀ ?

A) Reject H₀ if the standardized test statistic is greater than 2.575 or less than -2.575 .
B) Reject H₀ if the standardized test statistic is greater than 2.33 or less than -2.33 .
C) Reject H₀ if the standardized test statistic is greater than 1.96 or less than -1.96
D) Reject H₀ if the standardized test statistic is greater than 1.645 or less than -1.645

Question 25

The mean age of professors at a university is greater than 58.3 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

A) There is sufficient evidence to support the claim
B) There is sufficient evidence to reject the claim
C) There is not sufficient evidence to reject the claim
D) There is not sufficient evidence to support the claim

Question 26

The mean monthly gasoline bill for one household is greater than $150. If a hupothesis test is performed, how should you interpret a dicision that fails to reject the null hypothesis?

A) There is sufficient evidence to support the claim
B) There is sufficient evidence to reject the claim 11ec7dab_1c0d_d1c3_8ca2_2157a3539171_TB34225555_00
C) There is not sufficient evidence to reject the claim 11ec7dab_1c0d_d1c3_8ca2_2157a3539171_TB34225555_00
D) There is not sufficient evidence to support the claim 11ec7dab_1c0d_d1c3_8ca2_2157a3539171_TB34225555_00

Question 27

Find the critical value for a left-tailed test with α = 0.025.

A) -1.96
B) -2.24
C) -1.645
D) -2.575

Question 28

The dean of a major university claims that the mean number of hours students study at her University (perday) is at most 3.6 hours. If a hypothesis test is performed, how should you interpret a decision that rejects thenull hypothesis?

Question 29

The mean age of principals in a local school district is 50.2 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

A) There is sufficient evidence to reject the claim
B) There is not sufficient evidence to reject the claim
C) There is sufficient evidence to support the claim
D) There is not sufficient evidence to support the claim

Question 30

The mean monthly gasoline bill for one household is greater than $160. If a hupothesis test is performed, how should you interpret a dicision that fails to reject the null hypothesis?

A) There is not sufficient evidence to support the claim
B) There is sufficient evidence to reject the claim
C) There is not sufficient evidence to reject the claim 11ec7daa_4623_17f2_8ca2_85a625d2b428_TB34225555_00
D) There is sufficient evidence to support the claim 11ec7daa_4623_17f2_8ca2_85a625d2b428_TB34225555_00

Question 31

If we do not reject the null hypothesis when the null hypothesis is in error, then we have made a

A) Type II error
B) Type I error
C) Correct decision
D) Type β error

Question 32

Find the critical value for a two-tailed test with α = 0.08.

A) ±1.75
B) ±1.405
C) ±2.65
D) ±1.96

Question 33

The mean age of professors at a university is 57.9 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

A) There is not sufficient evidence to reject the claim
B) There is sufficient evidence to reject the claim
C) There is sufficient evidence to support the claim
D) There is not sufficient evidence to support the claim

Question 34

We never conclude "Accept H₀ " in a test of hypothesis. This is because:

A) =p (Type II error) is not known.
B) is the probability of a Type I error.
C) The rejection region is not known.
D) The p-value is not small enough.

Question 35

The mean number of rushing yards for one NFL team was less than 109 yards per game. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

A) There is not sufficient evidence to support the claim
B) There is sufficient evidence to reject the claim
C) There is not sufficient evidence to reject the claim
D) There is sufficient evidence to support the claim

Question 36

If we reject the null hypothesis when the null hypothesis is true, then we have made a

A) Type I error
B) Type II error
C) Correct decision
D) Type α error

Question 37

The dean of a major university claims that the mean number of hours students study at her University (perday) is at most 4.4 hours. If a hypothesis test is performed, how should you interpret a decision that fails toreject the null hypothesis?

Question 38

The mean number of rushing yards for one NFL team was less than 99 yards per game. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

A) There is sufficient evidence to support the claim
B) There is sufficient evidence to reject the claim
C) There is not sufficient evidence to reject the claim
D) There is not sufficient evidence to support the claim

Question 39

The level of significance, α, is the probability of making a

A) Type I error
B) Type II error
C) Correct decision
D) Type β error

Question 40

True or False: Type I and Type II errors are independent events.

Question 41

Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claimsthat more than 80% of firms in the manufacturing sector still do not offer any child-care benefits to theirworkers. A random sample of 390 manufacturing firms is selected and asked if they offer child-care benefits.Suppose the P-value for this test was reported to be p = 0.1112. State the conclusion of interest to the union.Use α = 0.10.

Question 42

When the results of a hypothesis test are determined to be statistically significant, then we _______________ thenull hypothesis.

A) reject
B) fail to reject
C) polarize
D) compartmentalize

Question 43

Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claimsthat more than 85% of firms in the manufacturing sector still do not offer any child-care benefits to theirworkers. A random sample of 430 manufacturing firms is selected, and only 32 of them offer child-carebenefits. Specify the rejection region that the union will use when testing at α = 0.10.

Question 44

A survey claims that 9 out of 10 doctors (i.e., 90 % ) recommend brand Z for their patients who have children. To test this claim against the alternative that the actual proportion of doctors who recommend brand Z 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) level?

A) a) yes; b) yes; c) no
B) a) yes; b) yes; c) yes
C) a) no; b) no; c) no
D) a) no; b) no; c) yes

Question 45

Suppose you want to test the claim that Given a sample size of n=35 and a level of significance of =0.01 , when should you reject H₀ ?

A) Reject H₀ if the standardized test statistic is less than -2.33 .
B) Reject H₀ if the standardized test is less than -2.575 .
C) Reject H₀ if the standardized test statistic is less than -1.96 .
D) Reject H₀ if the standardized test statistic is less than -1.28 .

Question 46

Determine the standardized test statistic, z , to test the claim about the population proportion given

A) -0.45
B) -1.645
C) -0.568
D) -0.124

Question 47

Determine the critical value, to test the claim about the population proportion p=0.250 given n=48 and

A)
B)
C)
D)

Question 48

Test the claim about the population proportion p ≥ 0.700 given n=50 and

Question 49

Fifty percent of registered voters in a congressional district are registered Democrats. The Republican candidatetakes a poll to assess his chances in a two-candidate race. He polls 1200 potential voters and finds that 621 planto vote for the Democratic candidate. Does the Republican candidate have a chance to win? Use α = 0.05.

Question 50

A survey claims that 9 out of 10 doctors (i.e., 90%) recommend brand Z for their patients who have children. Totest this claim against the alternative that the actual proportion of doctors who recommend brand Z is less than90%, a random sample of 100 doctors results in 83 who indicate that they recommend brand Z. The test statisticin this problem is approximately (round to the nearest hundredth):

A) -2.33
B) 2.33
C) -1.83
D) -1.99

Question 51

In a sample, 76 people or 38% of the people in the sample said that the mayor should be prosecuted formisconduct. How many people where in the sample?

A) 200
B) 29
C) 105
D) 50

Question 52

A recent study claimed that at least 15 % of junior high students are overweight. In a sample of 160 students, 18 were found to be overweight. At α=0.05 , test the claim.

Question 53

The business college computing center wants to determine the proportion of business students who havepersonal computers (PCʹs) at home. If the proportion exceeds 30%, then the lab will scale back a proposedenlargement of its facilities. Suppose 300 business students were randomly sampled and 65 have PCʹs at home.What assumptions are necessary for this test to be satisfied?

A) No assumptions are necessary.
B) The sample variance equals the population variance.
C) The population has an approximately normal distribution.
D) The sample mean equals the population mean.

Question 54

A nationwide survey claimed that at least 55% of parents with young children condone spanking their child asa regular form of punishment. In a random sample of 100 parents with young children, how many would needto say that they condone spanking as a form of punishment in order to refute the claim at α = 0.5?

A) You would need 46 or less parents to support spanking to refute the claim.
B) You would need exactly 46 parents to support spanking to refute the claim.
C) You would need 47 or less parents to support spanking to refute the claim.
D) You would need more than 46 parents to support spanking to refute the claim.

Question 55

A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 15% ofthe women who actually have the disease. A new method has been developed that researchers hope will beable to detect cancer more accurately. A random sample of 80 women known to have breast cancer werescreened using the new method. Of these, the new method failed to detect cancer in 9. Is the sample sizesufficiently large in order to conduct this test of hypothesis? Explain. Round to the nearest thousandth.

Question 56

The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion exceeds 35% , then the lab will scale back a proposed enlargement of its facilities. Suppose 300 business students were randomly sampled and 85 have PC's at home. Find the rejection region for this test using =0.10 .

A) Reject
B) Reject
C) Reject
D) Reject

Question 57

A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 15% ofthe women who actually have the disease. A new method has been developed that researchers hope will beable to detect cancer more accurately. A random sample of 70 women known to have breast cancer werescreened using the new method. Of these, the new method failed to detect cancer in 8. Calculate the teststatistic used by the researchers for this test of hypothesis. Round to the nearest thousandth.

Question 58

Suppose you want to test the claim that Given a sample size of n=53 and a level of significance of when should you reject H₀ ?

A) Reject H₀ if the standardized test statistic is greater than 2.33 .
B) Reject H₀ if the standardized test statistic is greater than 1.96 .
C) Reject H₀ if the standardized test statistic is greater than 2.575 .
D) Reject H₀ if the standardized test statistic is greater than 1.645 .

Question 59

An airline claims that the no-show rate for passengers is less than 5 % . In a sample of 420 randomly selected reservations, 19 were no-shows. At α = 0.01, test the airline's claim. Round to the nearest thousandth when calculating the test statistic.

Question 60

The business college computing center wants to determine the proportion of business students who havepersonal computers (PCʹs) at home. If the proportion differs from 35%, then the lab will modify a proposedenlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is 2.6. Find the P-valuefor a two-tailed test of hypothesis.

A) 0.0094
B) 0.0047
C) 0.4906
D) 0.4953

Question 61

According to a local chamber of commerce, in 1993, 5.9% of local area residents owned more than five cars. Alocal car dealer claims that the percentage has increased. He randomly selects 180 local area residents and findsthat 12 of them own more than five cars. Test this car dealerʹs claim at the α = 0.05 level of significance.

Question 62

The weekly salaries (in dollars) of randomly selected employees of a company are summarized in the boxplotbelow. Based on the boxplot, is a large sample necessary to conduct a hypothesis test about the mean salary? Ifso, why?

A) Yes; data do not appear to be normally distributed but skewed right.
B) Yes; data do not appear to be normally distributed but skewed left.
C) No; data appear to be normally distributed.
D) Yes; data contain outliers.

Question 63

Find the standardized test statistic t for a sample with your answer to three decimal places.

A) 1.667
B) 1.997
C) 1.452
D) 1.239

Question 64

According to a prestigious historical society, in 1999, 7.2% of recent high school graduates believe that theRomans invented mayonnaise. A classics scholar believes that the percentage has increased since then. Herandomly selects 125 recent high school graduates and finds that 17 of them believe in the Roman invention ofmayonnaise. Test this researcherʹs claim at the α = 0.01 level of significance.

Question 65

Find the standardized test statistic t for a sample with your answer to three decimal places.

A) 1.890
B) 1.991
C) 2.132
D) 2.001

Question 66

The engineering school at a major university claims that 20 % of its graduates are women. In a graduating class of 210 students, 58 were females. Does this suggest that the school is believable? Use α=0.05 . Round to the nearest ten-thousandth when calculating the test statistic.

Question 67

The ages of a group of patients being treated at one hospital for osteoporosis are summarized in the frequencyhistogram below. Based on the histogram, is a large sample necessary to conduct a hypothesis test about themean age? If so, why?

A) Yes; data do not appear to be normally distributed but skewed left.
B) Yes; data do not appear to be normally distributed but skewed right.
C) Yes; data do not appear to be normally distributed but bimodal.
D) No; data appear to be normally distributed with no outliers.

Question 68

Find the standardized test statistic t for a sample with Round your answer to three decimal places.

A) -0.894
B) -0.872
C) -1.265
D) -1.233

Question 69

Determine the critical value for a left-tailed test of a population mean at the α = 0.005 level of significancebased on a sample size of n = 30.

A) -2.756
B) -1.699
C) 2.756
D) 2.750

Question 70

3 Test hypotheses about a population proportion using the binomial probability distribution.

Question 71

Determine the critical value for a right-tailed test of a population mean at the α = 0.001 level of significancewith 15 degrees of freedom.

A) 3.733
B) 2.602
C) -3.733
D) 3.787

Question 72

According to a national statistics bureau, 3.7% of males living in the Southwest were retired exterminators. Aresearcher believes that the percentage has increased since then. She randomly selects 250 males in theSouthwest and finds that 4 of them are retired exterminators. Test this researcherʹs claim at the α = 0.1 level ofsignificance.

Question 73

Determine the critical values for a two-tailed test of a population mean at the α = 0.01 level of significancebased on a sample size of n = 29.

A) ±2.763
B) ±2.756
C) ±2.467
D) ±2.462

Question 74

An event is considered unusual if the probability of observing the event is

A) less than 0.05
B) less than 0.025
C) less than 0.10
D) greater than 0.95

Question 75

A relative frequency histogram for the sale prices of homes sold in one city during 2010 is shown below. Basedon the histogram, is a large sample necessary to conduct a hypothesis test about the mean sale price? If so,why?

A) Yes; data do not appear to be normally distributed but skewed right.
B) Yes; data do not appear to be normally distributed but skewed left.
C) No; data appear to be normally distributed.
D) Yes; data do not appear to be normally distributed but bimodal.

Question 76

Find the standardized test statistic t for a sample with Round your answer to three decimal places.

A) -0.825
B) -0.008
C) -0.037
D) -0.381

Question 77

The weights (in ounces) of a sample of tomatoes of a particular variety are summarized in the boxplot below.Based on the boxplot, is a large sample necessary to conduct a hypothesis test about the mean weight? If so,why?

A) Yes; data contain outliers.
B) Yes; data do not appear to be normally distributed but skewed left.
C) Yes; data do not appear to be normally distributed but skewed right.
D) No; data appear to be normally distributed with no outliers.

Question 78

Find the standardized test statistic t for a sample with your answer to three decimal places.

A) -2.189
B) -3.186
C) -3.010
D) -2.617

Question 79

A coin is tossed 1000 times and 570 heads appear. At α = 0.05, test the claim that this is not a biased coin.

Question 80

Find the standardized test statistic t for a sample with your answer to three decimal places.

A) 1.452
B) 1.728
C) 1.631
D) 1.312