Deck 7: Hypothesis Testing

Question 1

For fixed sample sizes, the t-statistic is more variable than the z-statistic.

Answer 1

True

Question 2

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.

Answer 2

True

Question 3

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

Answer 3

D

Question 4

The power of a test measures the sensitivity of the test to detect a real difference in parameters if one
actually exists.

Question 5

Sam Ying, a career counsellor, 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 years and a standard deviation of 1.5 years. The test
value would be -2.68.

Question 6

A type I error can occur when the null hypothesis is not rejected.

Question 7

There is one, and only one, correct method to perform a hypothesis test procedure.

Question 8

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

Question 9

Question 10

When conducting a two-tailed z.-test with , the test value was 2.07. The decision would be: do
not reject the null hypothesis.

Question 11

Stating the hypothesis is the first step used in hypothesis testing.

Question 12

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

Question 13

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.

Question 14

Question 15

Using z the table found in Table E of Appendix C, the critical value for the right-tailed test with is 1.88.

Question 16

The probability of committing a type II error is symbolized by b.

Question 17

Evaluating the data should occur after summarizing the results of performing a hypothesis test.

Question 18

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 19

The chi-square critical value for when the test is left-tailed is 5.812.

Question 20

An assumption of the chi-square test for a single variance is that the observations must be independent of
each other.

Question 21

For the conjecture, "The average weight of a cuckoo bird is less than or equal to 2.5 pounds," the null and alternative hypotheses are:

Question 22

For the conjecture, "The average age of students in this class is 21," the null hypothesis is:

A) We accept the hypothesis that the average age of students in this class is 21
B) The average age of students in this class is 21
C) The average age of students in this class is not 21
D) We reject the hypothesis that he average age of students in this class is 21

Question 23

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

A) No, there are no parameters contained in these statements
B) No, l cannot be a parameter
C) Yes, these statements have two non-overlapping hypotheses and compare a parameter to a value
D) Yes, these statements have two non-overlapping hypotheses and compare two parameters

Question 24

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?

Question 25

Question 26

If the observed value is 7, the expected value is 3, and the standard error is 4, then the test value used for the z test is equal to

A) 1.00
B) 4.00
C) -4.00
D) -1.00

Question 27

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 28

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

A) j
B) b
C) h
D) α

Question 29

Question 30

Are the following statements a valid pair of 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 31

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

A) 0.5577
B) 0.7774
C) 1.1155
D) 1.5548

Question 32

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

A) No, there are no parameters contained in these statements
B) No, the alternative hypothesis cannot contain numeric values
C) No, these statements have overlapping regions
D) No, these statements both compare a parameter to a value

Question 33

Using the z table in Table E of Appendix C, determine the critical value for the left-tailed test with 0.02.

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

Question 34

The Natural Resources Canada Web site said that the national average price of regular gasoline was $1.058 per litre on July 3, 2007. It was felt that the price of gasoline in Toronto was significantly lower
Than the national average. A survey of ten different gas stations in Toronto, Ontario found the average
Price of gasoline to be $1.028 per litre with a standard deviation of $0.0263. What is the critical value
Using ?

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

Question 35

Using the z table in Table E of Appendix C, determine the critical value for the right-tailed test with α = 0.035.

A) 0.39
B) 2.05
C) 1.81
D) 2.11

Question 36

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

Question 37

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

A) -2.1444
B) -1.4051
C) -0.9945
D) -0.4973

Question 38

Using the z table in Table E of Appendix C, what are the critical values for a two-tailed test when 0.03.

Question 39

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 40

Question 41

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 , what is the test value?

A) 1.96
B) 1.5
C) -1.5
D) 1.64

Question 42

If the observed value is 4, the expected value is 5, and the standard error is 3, then the test value used for the z test is equal to

A) 0.33
B) 1.00
C) -1.00
D) -0.33

Question 43

At a certain American university, the average attendance at basketball games has been 2,700 spectators per game. The attendance for the first 16 games has been 2,450 spectators per game with a standard
Deviation of 550. The athletic director claims that the attendance is the same as last year. If , what
Are the critical values?

Question 44

At a certain university, the average attendance at basketball games has been 1,000 spectators per game. Due to the dismal showing of the team this year, the attendance for the first four games has been only 700
Spectators per game with a standard deviation of 200. The athletic director claims that the attendance is
The same as last year. If , what is the test statistic?

A) -3.00
B) -6.00
C) -7.00
D) -9.00

Question 45

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. Is there evidence that the costs of homes for sale in this subdivision are
actually lower than claimed?
At , what is the test value?

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

Question 46

Doctors nationally believe that 72% of a certain type of operation are successful. In a certain hospital, 53 of these operations were observed, and 63% of them were successful. If , 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.

Question 47

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. Is there evidence that the costs of homes for sale in this subdivision are
actually lower than claimed?
At a certain university, the average cost of books per student was $390 per student last semester. In a sample of 60 students this semester, their average cost was $425 with a standard deviation of $75.
The Dean of Students believes that the costs are greater this semester. What is the test statistic for this
Hypothesis?

A) 0.47
B) 0.58
C) 3.61
D) 28.00

Question 48

According to Statistics Canada, the average age of a groom was 34.5 years in 2003. A sample of 16 prospective grooms in St. Johns revealed that their average age was 34.9 years with a standard deviation
Of 5.3 years. At , what is the test value?

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

Question 49

A political strategist believes that 56% of voters in a certain province support his candidate. He then commissions a poll of 800 voters and 53% of them support his candidate. If , is the political
Strategist's belief warranted?

A) Yes, because the test value -1.01 is in the noncritical region.
B) Yes, because the test value -1.88 is in the critical region.
C) No, because the test value -1.88 is in the noncritical region.
D) No, because the test value -1.71 is in the noncritical region.

Question 50

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. Is there evidence that the costs of homes for sale in this subdivision are
actually lower than claimed?
What is the p-value for a one-sided test of the data provided above?

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

Question 51

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. Is there evidence that the costs of homes for sale in this subdivision are
actually lower than claimed?
In a particular city, the average salary of secretaries is $29,000 per year. Secretaries at Company A claim that they are paid less than the city average. In a sample of 50 secretaries, their average salary was
$25,000 per year with a standard deviation of $5,000. What is the test statistic for this hypothesis?

A) -5.66
B) -0.80
C) 0.80
D) 5.66

Question 52

What is the critical t-value for a right-tailed test when and ?

A) 2.179
B) 2.831
C) 2.228
D) 1.869

Question 53

An average computer mouse inspector can inspect 40 mice per hour. The 46 computer mice inspectors at a particular factory can only inspect 36 mice per hour with a standard deviation of 8. Does the company
Have reason to believe that these inspectors are slower than average?

A) Yes, because -3.39 falls in the noncritical region
B) No, because -1.95 falls in the critical region
C) Yes, because -3.39 falls in the critical region
D) No, because -1.95 falls in the noncritical region

Question 54

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. Is there evidence that the costs of homes for sale in this subdivision are
actually lower than claimed?
An average department store sells 200 men's suits per year. The men's suit departments at a particular national chain of stores claim that they more than the industry average. In a sample of 50 stores, they
Sold, on the average, 280 suits per year with a standard deviation of $40. What is the test statistic for this
Hypothesis?

A) 0.28
B) 2.00
C) 8.07
D) 14.14

Question 55

A recent report from the American Medical Association claims that for the first time in 10 years, the average salary of psychiatrists was $189,121 with a standard deviation of $26,975. A random sample
Of 25 Canadian psychiatrists this year yielded an average salary of $198,630. Is there evidence that the
Average salary is actually higher than what the American Medical Association reported (assume that the
Variation in Canadian salaries is the same as that in the US)? What is the p-value for a one-sided test?

A) 0.0024
B) 0.0035
C) 0.1328
D) 0.0390

Question 56

The average speed of greyhound dogs is about 18.9 meters per second. A particular greyhound breeder claims that her dogs are faster than the average greyhound. In a sample of 40 of her dogs, they ran, on the
Average, 19.4 meters per second with a standard deviation of 1.4. Is her claim correct?

A) Yes, because 0.06 falls in the critical region
B) No, because 0.06 falls in the critical region
C) Yes, because 2.26 falls in the critical region
D) No, because 0.5 falls in the critical region

Question 57

What are the critical t-values for a two-tailed test when ?

Question 58

Nationwide, the average waiting time until an electric utility customer service representative answers a call is 200 seconds per call. The Gigantic Kilowatt Energy Company took a sample of 40 calls and found
That, on the average, they answered in 140 seconds per call with a standard deviation of $30. Can the
Company claim that they are faster than the average utility?

A) Yes, because -12.65 falls in the critical region
B) No, because -2.00 falls in the critical region
C) Yes, because -0.32 falls in the noncritical region
D) No, because -0.32 falls in the critical region

Question 59

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.
Give the p-value for the data provided above.

A) 0.4987
B) 0.0084
C) 0.1325
D) 0.0668

Question 60

A recent study claims that business travelers spend an average of $41 per day on meals. A sample of 16 business travelers found that they had spent an average of $45 per day with a standard deviation of $3.65.
If , what are the critical values?

Question 61

A scientist has a theory that 36% of geese in his area do not fly south for the winter. He tags 65 random geese in the summer and finds that 38% of them do fly south. If , is the scientist's belief
Warranted?

A) Yes, because the test value -4.37 is in the critical region.
B) No, because the test value -4.80 is in the noncritical region.
C) Yes, because the test value 4.80 is in the critical region.
D) No, because the test value 4.37 is in the critical region.

Question 62

One of the assumptions for the chi-square test for a single variance is that the __________ must be
normally distributed for the variable under study.
________________________________________

Question 63

Assume that a 99% confidence interval for the mean is (17.0, 19.0). Then a hypothesis test of would result in

A) Rejecting the null hypothesis because 16.0 is less than 17.0
B) Accepting the null hypothesis because 16.0 is less than 19.0
C) Accepting the null hypothesis because 19.0 is more than 17.0
D) There is insufficient information to make any conclusions about the hypothesis test

Question 64

A lumber mill is tested for consistency by measuring the variance of board thicknesses. The target accuracy a variance of 0.0015 or less. If 22 measurements are taken and their variance is 0.006, is there
Enough evidence to reject the claim that her standard deviation is within the limit at ?

A) Yes, comparing the test value 84.00 and the critical value 38.93.
B) No, comparing the test value 18.33 and the critical value 38.93.
C) Yes, comparing the test value 84.00 and the critical value 40.29.
D) No, comparing the test value 18.33 and the critical value 40.29.

Question 65

Assume that in a hypothesis test with null hypothesis , that a value of 11.0 for the sample mean results in the null hypothesis being rejected. That corresponds to a confidence interval result
Of

A) The 95% confidence interval for the mean contains the value 11.0
B) The 95% confidence interval for the mean contains the value 14.0
C) The 95% confidence interval for the mean does not contain the value 14.0 D There is insufficient information to conclude whether the 95% confidence interval for the mean
) contains or does not contain the value 14.0

Question 66

Which of the following is true?

A) The smaller the P-value, the stronger is the evidence against the null hypothesis.
B) For fixed sample size, increasing the alpha error increases the beta error.
C) If the type I error is held constant, increasing the sample size increases the type II error.
D) The power of a test equals a + b.

Question 67

A random sample of 25 rats was fed a diet for a period of 4 weeks. The weight gain (in grams) was recorded for each rat. The average weight gain was 16.4 with a corresponding standard deviation of 3.0.
The P-value for testing the claim that this diet would increase weight by at least 15 grams would be

A) 0.005
B) 0.003
C) 0.014
D) 0.135

Question 68

A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy a standard deviation of 1.3 or less. If 18 measurements are
Taken and their standard deviation is 1.6, is there enough evidence to reject the claim that her standard
Deviation is within the limit at ?

A) No, comparing the test value 5.07 and the critical value 5.90.
B) Yes, comparing the test value 20.92 and the critical value 5.78.
C) No, comparing the test value 25.75 and the critical value 33.41.
D) Yes, comparing the test value 20.92 and the critical value 5.90.

Question 69

A statistician believes that the standard deviation of the weights of firemen is less than 25 pounds. A sample of 20 firemen had a standard deviation of 23.2 pounds. Assume that the variable is normally
Distributed with . What is the critical value?

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

Question 70

If the type II error in a hypothesis test with , then the power of this test is

A) 0.05
B) 0.30
C) 0.70
D) 0.95

Question 71

Assume that in a hypothesis test with null hypothesis , that a value of 13.0 for the sample mean results in the null hypothesis being accepted. That corresponds to a confidence interval
Result of

A) The 98% confidence interval for the mean contains the value 13.0
B) The 98% confidence interval for the mean contains the value 17.0
C) The 98% confidence interval for the mean does not contain the value 17.0 D There is insufficient information to conclude whether the 98% confidence interval for the mean
) contains or does not contain the value 17.0

Question 72

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

Question 73

Assume that in a hypothesis test with null hypothesis , that a value of 11.0 for the sample mean results in the null hypothesis being accepted. That corresponds to a confidence interval
Result of

A) The 0.10% confidence interval for the mean contains the value 11.0
B) The 90% confidence interval for the mean contains the value 14.0
C) The 90% confidence interval for the mean does not contain the value 14.0
D)There is insufficient information as to if the 90% confidence interval for the mean does or does not contain the value 11.0

Question 74

Assume that in a hypothesis test with null hypothesis , that a value of 17.0 for the sample mean results in the null hypothesis being rejected. That corresponds to a confidence interval result
Of

A) The 10% confidence interval for the mean contains the value 17.0
B) The 90% confidence interval for the mean contains the value 17.0
C) The 90% confidence interval for the mean does not contain the value 13.0
D)There is insufficient information as to if the 90% confidence interval for the mean does or does not contain the value 17.0

Question 75

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

Question 76

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

Question 77

A doctor believes that the standard deviation of systolic blood pressure is 15 mmHg. A random sample of 24 patients found a standard deviation of 23. Assume the variable is normally distributed and What are the critical 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 78

Assume that a 99% confidence interval for the mean is (11.5, 13.0). Then a hypothesis test of would result in

A) Accepting the null hypothesis because 12.0 is less than 13.0
B) Accepting the null hypothesis because 12.0 is between 11.5 and 13.0
C) Rejecting the null hypothesis if because 12.0 is more than 11.5
D) There is insufficient information to make any conclusions about the hypothesis test

Question 79

A random sample of 25 rats was fed a diet for a period of 4 weeks. The weight gain (in grams) was recorded for each rat. It is known that the population variance is 4. The average weight gain was 16.1.
The P-value for testing the claim that this diet would increase weight by at least 15 grams would be

A) 0.005
B) 0.003
C) 0.014
D) 0.135

Question 80

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