Deck 8: Hypothesis Testing

Question 1

Which type of null hypothesis is used in the figure below?

A)
B)
C)
D)

Answer 1

A

Question 2

The null hypothesis states that there is no difference between a parameter and a specific value, or that there is no difference between two parameters.

Answer 2

True

Question 3

Are the following statements and a valid pair of null and alternative hypothesis?

A) No, the null hypothesis should not state an equality.
B) No, cannot be a parameter
C) Yes, the null hypothesis specifies an equality and the alternative specifies a difference.
D) Yes, the alternative hypothesis specifies an equality and the null hypothesis specifies a difference.

Answer 3

C

Question 4

Sandra Johnson, a researcher, believes her pulse rate will decrease with exercise. Her alternative hypothesis would contain an equal sign.

Question 5

Which type of null hypothesis is used in the figure below?

A)
B)
C)
D)

Question 6

In a(n) _____________ test, the null hypothesis should be rejected when the test value is in either of the two critical regions.

Question 7

Which type of alternative hypothesis is used in the figure below?

A)
B)
C)
D)

Question 8

A type I error occurs if one rejects the null hypothesis when it is __________.

Question 9

If the null hypothesis is not rejected when it is false, a type II error has occurred.

Question 10

A right-tailed test is used when .

Question 11

Is the statement a valid null hypothesis?

A) Yes, this is a statement that compares a parameter to a value.
B) Yes, this is a statement that compares two parameters.
C) No, equalities are not permitted in a null hypothesis.
D) No, there is no parameter contained in this statement.

Question 12

The probability of a type I error is represented by which of the following symbols?

A) φ
B) β
C) η
D) α

Question 13

Stating the hypothesis should be the first step used in hypothesis testing.

Question 14

Are the following statements and valid null and alternative hypotheses?

A) No, there are no parameters contained in these statements.
B) No, the alternative hypothesis cannot contain numeric values.
C) Yes, these statements are two non-overlapping hypotheses and compare two parameters.
D) Yes, these statements are two non-overlapping hypotheses and compare a parameter to a value.

Question 15

In performing a hypothesis test, one should decide whether to reject or not reject the null hypothesis before summarizing the results.

Question 16

A type II error occurs if one does not reject the null hypothesis when it is __________.

Question 17

Is the statement a valid null hypothesis?

A) Yes, this is a statement that compares a parameter to a value.
B) Yes, this is a statement that compares two parameters.
C) No, equalities are not permitted in a null hypothesis.
D) No, there is no parameter contained in this statement.

Question 18

Using the z table, find the critical value (or values) for an = 0.03 two-tailed test.

A) 1.88
B) 2.17
C) 1.88
D) 2.17

Question 19

The numerical value obtained from a statistical test is called the _______________.

Question 20

Is the statement a valid null hypothesis?

A) Yes, this is a statement that compares a parameter to a value.
B) Yes, this is a statement that compares two parameters.
C) No, equalities are not permitted in a null hypothesis.
D) No, there is no parameter contained in this statement.

Question 21

Using the z table, determine the critical values for a two-tailed test when α = 0.03.

A) ± 1.88
B) ± 2.17
C) ± 0.18
D) ± 0.06

Question 22

Alyson Silvastein, a scientist, reports that the average number of hours a person can go without sleep and still function normally is 29 with a standard deviation of five hours. A sample of 49 people had an average of 31 hours that they could go without sleep and still function normally. The test value for this hypothesis would be 2.8.

Question 23

A garbage collector believes that he averages picking up more than four tons of garbage per day. What is the null hypothesis for his statement?

A)
B)
C)
D)

Question 24

Using the z table, find the critical value (or values) for an = 0.12 right-tailed test.

A) 0.59
B) 0.78
C) 1.18
D) 1.56

Question 25

If the sample mean is 7, the hypothesized population mean is 4, and the population standard deviation is 2, compute the test value needed for the z test.

A) 1.50
B) 3.00
C) -3.00
D) -1.50

Question 26

A recent survey of gasoline prices indicated that the national average was $4.098 per gallon. The Dallas Automobile Club claimed that gasoline in Texas was significantly lower than the national average. A survey covering 10 different suburbs in Dallas found the average price of gasoline to be $3.924 per gallon with a population standard deviation of $0.053. What critical value should be used to test the claim using α = 0.01?

A) 1.26
B) 2.33
C) -1.26
D) -2.33

Question 27

For the conjecture "The average age of students in this class is 20", the null hypothesis is:

A) We accept the hypothesis that the average age of students in this class is 20.
B) The average age of students in this class is 20.
C) The average age of students in this class is not 20.
D) We reject the hypothesis that the average age of students in this class is 20.

Question 28

When conducting a two-tailed z test with α = 0.01, the test value was computed to be 2.07. The decision would be to not reject the null hypothesis.

Question 29

For the conjecture "The average weight of a cuckoo bird is less than 1.3 pounds", the null and alternative hypotheses are:

A) The average weight of a cuckoo bird is less than or equal to 1.3 pounds. The average weight of a cuckoo bird is less than 1.3 pounds.
B) The average weight of a cuckoo bird is equal to 1.3 pounds. The average weight of a cuckoo bird is less than 1.3 pounds.
C) The average weight of a cuckoo bird is more than 1.3 pounds. The average weight of a cuckoo bird is less than 1.3 pounds.
D) The average weight of a cuckoo bird is less than $1.3 pounds. The average weight of a cuckoo bird is more than or equal to $1.3 pounds.

Question 30

Use the following to answer questions :
The Eagle Ridge Contractors Association claims the average price of a home in their subdivision is $125,150 with a standard deviation of $7,350. A sample of 36 homes for sale in this subdivision had an average selling price of $123,550. The Eagle Ridge Home Owners Association is interested in knowing if the costs of homes for sale in this subdivision are actually lower than claimed?
What is the p-value for this left-tailed test?

A) 0.0853
B) 0.0951
C) 0.1327
D) 0.0036

Question 31

Use the following to answer questions:
A recent survey indicated that the average amount spent for breakfast by business managers was $7.58 with a standard deviation of $0.42. It was felt that breakfasts on the West Coast were higher than $7.58. A sample of 81 business managers on the West Coast had an average breakfast cost of $7.65.
At α = 0.05, what is the critical value?

A) 1.96
B) 1.5
C) -1.5
D) 1.65

Question 32

Using the z table, determine the critical value for the left-tailed test with α = 0.02.

A) 2.33
B) 2.05
C) -2.33
D) -2.05

Question 33

If the sample mean is 8, the hypothesized population mean is 11, and the population standard deviation is 2, compute the test value needed for the z test.

A) 1.50
B) 3.00
C) -3.00
D) -1.50

Question 34

Dr. Christina Cuttleman, a nutritionist, claims that the average number of calories in a serving of popcorn is 75 with a standard deviation of 7. A sample of 50 servings of popcorn was found to have an average of 78 calories. Check Dr. Cuttleman's claim at α = 0.05.

Question 35

Using the z table, determine the critical value for the right-tailed test with α = 0.035.

A) 0.35
B) 0.70
C) 1.81
D) 2.43

Question 36

Using the z table, find the critical value (or values) for an = 0.021 left-tailed test.

A) -2.03
B) -2.31
C) -1.01
D) -1.15

Question 37

The critical value for a right-tailed test with α = 0.03 is 1.88.

Question 38

For the conjecture "The average rent of an apartment is more than $900 per month," the alternative hypothesis is:

A) The average rent of an apartment is less than or equal to $900 per month.
B) The average rent of an apartment is greater than $900 per month.
C) We accept the hypothesis that the average rent of an apartment is more than $900 per month.
D) We reject the hypothesis that the average rent of an apartment is more than $900 per month.

Question 39

Use the following to answer questions :
The Eagle Ridge Contractors Association claims the average price of a home in their subdivision is $125,150 with a standard deviation of $7,350. A sample of 36 homes for sale in this subdivision had an average selling price of $123,550. The Eagle Ridge Home Owners Association is interested in knowing if the costs of homes for sale in this subdivision are actually lower than claimed?
Compute the test value?

A) -1.31
B) 1.31
C) -1.52
D) 1.52

Question 40

Use the following to answer questions:
A recent survey indicated that the average amount spent for breakfast by business managers was $7.58 with a standard deviation of $0.42. It was felt that breakfasts on the West Coast were higher than $7.58. A sample of 81 business managers on the West Coast had an average breakfast cost of $7.65.
Find the P-value for the test.

A) 0.4332
B) 0.2734
C) 0.1325
D) 0.0668

Question 41

An average department store sells 150 men's suits per year. The men's suit departments at a particular national chain of stores claim they sell more than the industry average. In 45 of their stores, they sold, on the average, 190 suits per year with a population standard deviation of 30. What is the test value for their claim?

A) 0.20
B) 1.33
C) 5.14
D) 8.94

Question 42

In a particular city, the average annual salary for secretaries is $31,000. A sample of 45 secretaries from Company A shows an average annual salary of $27,500 with a population standard deviation of $5,500. Secretaries at Company A claim they are paid less than the city average. What is the test value for this claim?

A) -4.27
B) -0.64
C) 0.64
D) 4.27

Question 43

Reginald Brown, an inspector from the Department of Weights and Measures, weighed 15 eighteen-ounce cereal boxes of corn flakes. He found their mean weight to be 17.8 ounces with a standard deviation of 0.4 ounces. At α = 0.01, are the cereal boxes lighter than they should be?

Question 44

State whether the null hypothesis should be rejected on the basis of the given P-value.
P-value = 0.235, , two-tailed test

A) Do not reject.
B) Reject.

Question 45

At a certain university, the average attendance at basketball games has been 2925. This year the attendance for the first 11 games has been 2715 with a standard deviation of 535. The athletic director claims that the attendance is the same as last year. If = .05, what are the critical values for this two-tailed t test?

A) 1.812
B) 2.228
C) 1.796
D) 2.201

Question 46

The average greyhound can reach a top speed of 18.5 meters per second. A particular greyhound breeder claims her dogs are faster than the average greyhound. A sample of 40 of her dogs ran, on average, 19.2 meters per second with a population standard deviation of 1.2 meters per second. With α = 0.05, is her claim correct?

A) Yes, because the test value 0.09 falls in the noncritical region.
B) No, because the test value 0.09 falls in the critical region.
C) Yes, because the test value 3.69 falls in the critical region.
D) No, because the test value 0.70 falls in the critical region.

Question 47

At a certain university, the average cost of books was $320 per student last semester and the population standard deviation was $85. This semester a sample of 55 students revealed an average cost of books of $355 per student. The Dean of Students believes that the costs are greater this semester. What is the test value for this hypothesis?

A) 0.41
B) 0.64
C) 3.05
D) 22.65

Question 48

An average computer mouse inspector can inspect 45 mice per hour with a population standard deviation of 14 mice per hour. The 44 computer mice inspectors at a particular factory can only inspect 38 mice per hour. Does the company have reason to believe that these inspectors are slower than average at α = 0.10?

A) Yes, because the test value -3.32 falls in the noncritical region.
B) No, because the test value -1.91 falls in the critical region.
C) Yes, because the test value -3.32 falls in the critical region.
D) No, because the test value -1.91 falls in the noncritical region.

Question 49

A manufacturer claims that its televisions have an average lifetime of at least five years (60 months) with a population standard deviation of seven months. Eighty-one televisions were selected at random, and the average lifetime was found to be 59 months. With α = 0.025, is the manufacturer's claim supported?

Question 50

State whether the null hypothesis should be rejected on the basis of the given P-value.
P-value = 0.172, , one-tailed test

A) Do not reject.
B) Reject.

Question 51

A recent report by the American Medical Association stated the average annual salary of psychiatrists is $189,121 with a population standard deviation of $26,975. A group of hospital administrators randomly sampled 64 psychiatrists and found an average annual salary of $198,630. The group claims that the average annual salary is actually higher than what the American Medical Association reported. What is the P-value for this one-sided test?

A) 0.0024
B) 0.0035
C) 0.1328
D) 0.0237

Question 52

Science fiction novels average 250 pages in length. The average length of 10 randomly chosen novels written by I. M. Wordy was 295 pages in length with a standard deviation of 60. At = .05, are Wordy's novels significantly longer than the average science fiction novel?

Question 53

According to Beautiful Bride magazine, the average age of a groom is now 26.2 years. A sample of 16 prospective grooms in Chicago revealed that their average age was 26.6 years with a standard deviation of 5.3 years. What is the test value for a t test of the claim?

A) 1.81
B) 0.30
C) 0.59
D) 2.13

Question 54

What is the critical value for a right-tailed t test when α = 0.025 and n = 13?

A) 2.179
B) 0.697
C) 0.695
D) 2.201

Question 55

The average magnesium concentration in ground water around Metro City is parts per million (ppm) with a standard deviation of . The table below shows the ground-water magnesium concentrations (ppm) from random sites in a suburb located 15 miles away. At , can it be concluded that the average magnesium concentration in the suburb differs from 86.2 ppm? a. State the hypotheses and identify the claim.
b. Find the critical values.
c. Compute the test statistic.
d. Make a decision.
e. Summarize the results.

Question 56

Find the P-value for the test value.
T = 1.581, n = 23, right-tailed

A) 0.0321
B) 0.1282
C) 0.0641
D) 0.0687

Question 57

A recent study of business travelers claims they spend an average of $41.00 per day on meals. As a test of this claim, a random sampling of 16 business travelers found they had spent an average of $45.00 per day with a standard deviation of $3.65. What are the critical values for a two-tailed t test of this claim with α = 0.05?

A) ± 2.120
B) ± 2.131
C) ± 1.753
D) ± 1.746

Question 58

What is the critical value for a two-tailed t test when α = 0.02 and n = 19?

A) 2.878
B) 2.567
C) 2.552
D) 2.110

Question 59

Sam Ying, a career counselor, claims the average number of years of schooling for an engineer is 15.8 years. A sample of 16 engineers had a mean of 15.0 years and a standard deviation of 1.5 years. The test value used in evaluating the claim would be -2.68.

Question 60

Nationwide, the average waiting time until a electric utility customer service representative answers a call is 210 seconds. The Gigantic Kilowatt Energy Company randomly sampled 30 calls and found that, on average, they were answered in 183 seconds with a population standard deviation of 30 seconds. Can the company claim that they are faster than the average utility at α = 0.05?

A) Yes, because the test value -4.93 falls in the critical region.
B) No, because the test value -0.90 falls in the critical region.
C) Yes, because the test value -0.16 falls in the critical region.
D) No, because the test value -0.16 falls in the critical region.

Question 61

A political strategist claims that 56% of voters in Madison County support his candidate. In a poll of 200 randomly selected voters, 100 of them support the strategist's candidate. At = .05, is the political strategist's claim warranted?

A) No, because the test value -1.01 is in the noncritical region.
B) No, because the test value -2.22 is in the critical region.
C) Yes, because the test value -2.22 is in the noncritical region.
D) Yes, because the test value -1.71 is in the noncritical region.

Question 62

The formula for the test value in a z test for proportions is __________.

Question 63

The χ² critical value for n = 16 and α = 0.01 for a left-tailed test is 5.812.

Question 64

A statistician claims that the standard deviation of the weights of firemen is less than 25 pounds. A sample of 20 randomly chosen firemen had a standard deviation of their weights of 26.2 pounds. Assume the variable is normally distributed. At α = 0.05, what is the critical value χ² for this test?

A) 31.410
B) 30.144
C) 10.851
D) 10.117

Question 65

It has been claimed that at UCLA at least 40% of the students live on campus. In a random sample of 250 students, 90 were found to live on campus. Does the evidence support the claim at = .01?

Question 66

A doctor claims that the standard deviation of systolic blood pressure is 12 mmHg. A random sample of 24 patients found a standard deviation of 14 mmHg. Assume the variable is normally distributed. At α = 0.01, what are the critical χ² values?

A) 9.262 and 44.181
B) 13.091 and 35.172
C) 13.848 and 36.415
D) 11.524 and 44.314

Question 67

Assume that a 99% confidence interval for the mean is . The null hypothesis at 0.01 would

A) not be rejected because 11.0 is less than 15.0.
B) not be rejected because 11.0 is between 9.0 and 15.0.
C) be rejected because 11.0 is more than 9.0.
D) be rejected because 11.0 is not equal to 12.00.

Question 68

Assume that a 90% confidence interval for the mean is . The null hypothesis at 0.10 would

A) be rejected because 17.0 is less than 18.5.
B) not be rejected because 17.0 is less than 21.5.
C) not be rejected because 21.5 is more than 18.5.
D) be rejected because 17.0 is not equal equal to 20.0.

Question 69

A lab technician is tested for her consistency by making multiple measurements of the cholesterol level in one blood sample. The target precision is a standard deviation of 1.4 mg/dL or less. If 16 measurements are taken and the standard deviation is 2.1 mg/dL, is there enough evidence to support the claim that her standard deviation is greater than the target, at = .01?

A) Yes, since the χ² test value 33.750 is greater than the critical value 32.000.
B) No, since the χ² test value 22.50 is less than the critical value 30.578.
C) Yes, since the χ² test value 33.750 is greater than the critical value 30.578.
D) No, since the χ² test value 22.50 is less than the critical value 32.000.

Question 70

A scientist claims that only 65% of geese in his area fly south for the winter. He tags 55 random geese in the summer and finds that 17 of them do not fly south in the winter. If = .05, is the scientist's belief warranted?

A) Yes, because the test value 0.64 is in the noncritical region.
B) No, because the test value 0.70 is in the critical region.
C) Yes, because the test value -0.70 is in the noncritical region.
D) No, because the test value -0.64 is in the noncritical region.

Question 71

A type I error is only a possibility when the null hypothesis is not rejected.

Question 72

If the null hypothesis is rejected at 0.05 when a mean of 15.0 is obtained from a random sample, one could also say that

A) the 5% confidence interval for the population mean contains the value 15.0.
B) the 95% confidence interval for the population mean contains the value 15.0.
C) the 95% confidence interval for the population mean does not contain the value 13.0.
D) the 5% confidence interval for the population mean does not contain the value 13.0.

Question 73

A lumber mill is tested for consistency by measuring the variance of board thickness. The target accuracy is a variance of 0.0035 square inches or less. If 30 measurements are made and their variance is 0.006 square inches, is there enough evidence to reject the claim that the standard deviation is within the limit at = .01?

A) Yes, since the χ² test value 49.71 is greater than the critical value 49.588.
B) No, since the χ² test value 9.23 is less than the critical value 49.588.
C) Yes, since the χ² test value 49.71 is less than the critical value 50.892.
D) No, since the χ² test value 9.23 is less than the critical value 50.892.

Question 74

A random sample of 450 shoppers at Quincy Mall found that 125 favored longer shopping hours. Is this sufficient evidence at the 0.05 level of significance to conclude that less than 30% of the shoppers at Quincy Mall favor longer hours?

Question 75

The probability of committing a type II error is denoted as β.

Question 76

At a certain university, the average attendance at basketball games has been 3225. Due to the dismal showing of the team this year, the attendance for the first 12 games has averaged only 2865 with a standard deviation of 735. The athletic director claims that the attendance is the same as last year. What is the test value needed to evaluate the claim?

A) -1.70
B) -3.79
C) -4.48
D) -5.88

Question 77

A machine fills 12-ounce bottles with soda. For the machine to function properly, the standard deviation of the sample must be less than or equal to 0.02 ounce. A sample of 8 bottles is selected, and the number of ounces of soda in each bottle is given. At , can you reject the claim that the machine is functioning properly? Justify your answer. (Assume that the variables are approximately normally distributed.)

A) , ; There is evidence to reject the claim that the machine is working properly.
B) , ; There is evidence to reject the claim that the machine is working properly.
C) , ; There is not enough evidence to reject the claim that the machine is working properly.
D) , ; There is evidence to reject the claim that the machine is working properly.

Question 78

Using Table G, find the P-value interval for the test value. , n = 11, right-tailed

A) 0.05 < P-value < 0.10
B) 0.1 < P-value < 0.20
C) 0.025 < P-value < 0.05
D) 0.90 < P-value < 0.95

Question 79

If the null hypothesis is not rejected at 0.01 when a mean of 7.0 is obtained from a random sample, one could also say that

A) the 1% confidence interval for the population mean contains the value 7.0.
B) the 99% confidence interval for the population mean contains the value 11.0.
C) the 99% confidence interval for the population mean does not contain the value 11.0.
D) the 1% confidence interval for the population mean does not contain the value 11.0.

Question 80

Doctors nationally believe that 74% of a certain type of operation are successful. In a particular hospital, 57 of these operations were observed and 47 of them were successful. At = .05, is this hospital's success rate different from the national average?

A) No, because the test value 0.86 is in the noncritical region.
B) Yes, because the test value 0.86 is in the critical region.
C) No, because the test value 1.46 is in the noncritical region.
D) Yes, because the test value 1.46 is in the noncritical region.