Deck 9: Hypothesis Tests

Question 1

In hypothesis testing, the hypothesis tentatively assumed to be true is

A)the alternative hypothesis
B)the null hypothesis
C)either the null or the alternative
D)None of the other answers are correct.

Answer 1

the null hypothesis

Question 2

A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is

A)H₀: $\mu$ $\lt$ 85 H_a: $\mu$ $\ge$ 85
B)H₀: $\mu$ $\le$ 85 H_a: $\mu$ $\gt$ 85
C)H₀: $\mu$$\ge$ 85 H_a: $\mu$ $\lt$ 85
D)None of the other answers are correct.

Answer 2

H₀: $\mu$$\ge$ 85 H_a: $\mu$ $\lt$ 85

Question 3

If the cost of a Type I error is high, a smaller value should be chosen for the

A)critical value
B)confidence coefficient
C)level of significance
D)test statistic

Answer 3

level of significance

Question 4

As a general guideline, the research hypothesis should be stated as the

A)null hypothesis
B)alternative hypothesis
C)tentative assumption
D)hypothesis the researcher wants to disprove

Question 5

Which of the following hypotheses applies to a situation where action must be taken both when H₀ cannot be rejected and when H₀ can be rejected?

A)
B)

C)

D)

Question 6

Your investment executive claims that the average yearly rate of return on the stocks she recommends is at least 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is

A)H₀: $\mu$ $\lt$ 10.0% H_a: $\mu$ $\ge$ 10.0%
B)H₀: $\mu$ $\le$ 10.0% H_a: $\mu$$\gt$ 10.0%
C)H₀: $\mu$ $\gt$ 10.0% H_a: $\mu$ $\le$ 10.0%
D)H₀: $\mu$ $\ge$ 10.0% H_a: $\mu$ $\lt$ 10.0%

Question 7

More evidence against H₀ is indicated by

A)lower levels of significance
B)smaller p-values
C)smaller critical values
D)lower probabilities of a Type II error

Question 8

In tests about a population proportion, p₀ represents the

A)hypothesized population proportion
B)observed sample proportion
C)observed p-value
D)probability of

Question 9

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any overfilling or underfilling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is

A)H₀: $\mu$ < 12 H_a: $\mu$ $\le$ 12
B)H₀: $\mu$ $\le$ 12 H_a: $\mu$ $\gt$ 12
C)H₀: $\mu$ $\neq$ 12 H_a: $\mu$ = 12
D)H₀: $\mu$ = 12 H_a: $\mu$ $\neq$ 12

Question 10

A meteorologist stated that the average temperature during July in Chattanooga was 80 degrees. A sample of 32 Julys was taken. The correct set of hypotheses is

A)H₀: $\mu$ $\lt$ 80 H_a: $\mu$ $\le$ 80
B)H₀: $\mu$$\le$ 80 H_a: $\mu$ > 80
C)H₀: $\mu$ $\neq$ 80 H_a: $\mu$ = 80
D)None of the other answers are correct.

Question 11

An example of statistical inference is

A)a population mean
B)descriptive statistics
C)calculating the size of a sample
D)hypothesis testing

Question 12

Which of the following is an improper form of the null and alternative hypotheses?

A)
B)

C)

D)

Question 13

A Type I error is committed when

A)a true alternative hypothesis is not accepted
B)a true null hypothesis is rejected
C)the critical value is greater than the value of the test statistic
D)sample data contradict the null hypothesis

Question 14

The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of its tires has increased. In order to test the validity of this belief, the correct set of hypotheses is

A)H₀: $\mu$ $\lt$ 40,000 H_a: $\mu$ $\ge$ 40,000
B)H₀: $\mu$ $\le$ 40,000 H_a: $\mu$ $\gt$ 40,000
C)H₀: $\mu$ $\gt$ 40,000 H_a: $\mu$$\le$ 40,000
D)H₀: $\mu$ $\ge$ 40,000 H_a: $\mu$ $\lt$ 40,000

Question 15

The manager of an automobile dealership is considering a new bonus plan in order to increase sales. Currently, the mean sales rate per salesperson is five automobiles per month. The correct set of hypotheses for testing the effect of the bonus plan is

A)H₀: $\mu$ $\lt$ 5 H_a: $\mu$ $\le$ 5
B)H₀: $\mu$ $\le$ 5 H_a: $\mu$ $\gt$ 5
C)H₀: $\mu$ $\gt$ 5 H_a: $\mu$ $\le$ 5
D)H₀: $\mu$ $\ge$ 5 H_a: $\mu$$\lt$ 5

Question 16

When the rejection region is in the lower tail of the sampling distribution, the p-value is the area under the curve

A)less than or equal to the critical value
B)less than or equal to the test statistic
C)greater than or equal to the critical value
D)greater than or equal to the test statistic

Question 17

For a two-tailed hypothesis test about $\mu$ , we can use any of the following approaches except

A)compare the confidence interval estimate of $\mu$ to the hypothesized value of $\mu$
B)compare the p-value to the value of $\alpha$
C)compare the value of the test statistic to the critical value
D)compare the level of significance to the confidence coefficient

Question 18

Two approaches to drawing a conclusion in a hypothesis test are

A)p-value and critical value
B)one-tailed and two-tailed
C)Type I and Type II
D)null and alternative

Question 19

In hypothesis testing, the alternative hypothesis is

A)the hypothesis tentatively assumed true in the hypothesis-testing procedure
B)the hypothesis concluded to be true if the null hypothesis is rejected
C)the maximum probability of a Type I error
D)All of the answers are correct.

Question 20

The practice of concluding "do not reject H₀" is preferred over "accept H₀" when we

A)are conducting a one-tailed test
B)are testing the validity of a claim
C)have an insufficient sample size
D)have not controlled for the Type II error

Question 21

If a hypothesis test leads to the rejection of the null hypothesis, a

A)Type II error must have been committed
B)Type II error may have been committed
C)Type I error must have been committed
D)Type I error may have been committed

Question 22

The level of significance in hypothesis testing is the probability of

A)accepting a true null hypothesis
B)accepting a false null hypothesis
C)rejecting a true null hypothesis
D)could be any of the above, depending on the situation

Question 23

In the hypothesis testing procedure, $\alpha$ is

A)the level of significance
B)the critical value
C)the confidence level
D)1 - level of significance

Question 24

Read the z statistics from the normal distribution table and circle the correct answer. A two-tailed test at a .0694 level of significance; z =

A)-1.96 and 1.96
B)-1.48 and 1.48
C)-1.09 and 1.09
D)-0.86 and 0.86

Question 25

Read the z statistic from the normal distribution table and circle the correct answer. A one-tailed test (upper tail) at a .123 level of significance; z =

A)1.54
B)1.96
C)1.645
D)1.16

Question 26

In order to test the hypotheses H₀: $\mu$ $\le$ 100 and H_a: $\mu$ $\gt$ 100 at an $\alpha$ level of significance, the null hypothesis will be rejected if the test statistic z is

A) $\ge$ z _$\alpha$
B) $\lt$ z _$\alpha$
C) $\le$ -z _$\alpha$
D) $\lt$ 100

Question 27

Read the z statistic from the normal distribution table and circle the correct answer. A one-tailed test (lower tail) at a .063 level of significance; z =

A)-1.86
B)-1.53
C)-1.96
D)-1.645

Question 28

The level of significance is the

A)maximum allowable probability of Type II error
B)maximum allowable probability of Type I error
C)same as the confidence coefficient
D)same as the p-value

Question 29

When the hypotheses H₀: $\mu$$\ge$ 100 and H_a: $\mu$ $\lt$ 100 are being tested at a level of significance of $\alpha$ , the null hypothesis will be rejected if the test statistic z is

A)> z _$\alpha$
B)> -z _$\alpha$
C)< -z _$\alpha$
D)< 100

Question 30

A two-tailed test is a

A)hypothesis test in which rejection region is in both tails of the sampling distribution
B)hypothesis test in which rejection region is in one tail of the sampling distribution
C)hypothesis test in which rejection region is only in the lower tail of the sampling distribution
D)hypothesis test in which rejection region is only in the upper tail of the sampling distribution

Question 31

For a two-tailed test with a sample size of 40, the null hypothesis will not be rejected at a 5% level of significance if the test statistic is

A)between -1.96 and 1.96, exclusively
B)greater than 1.96
C)less than 1.645
D)greater than -1.645

Question 32

For a one-tailed test (upper tail) with a sample size of 900, the null hypothesis will be rejected at the .05 level of significance if the test statistic is

A)less than or equal to -1.645
B)greater than or equal to 1.645
C)less than 1.645
D)less than -1.96

Question 33

In hypothesis testing, the critical value is

A)a number that establishes the boundary of the rejection region
B)the probability of a Type I error
C)the probability of a Type II error
D)the same as the p-value

Question 34

The error of rejecting a true null hypothesis is

A)a Type I error
B)a Type II error
C)can be either a or b, depending on the situation
D)committed when not enough information is available

Question 35

A one-tailed test is a

A)hypothesis test in which rejection region is in both tails of the sampling distribution
B)hypothesis test in which rejection region is in one tail of the sampling distribution
C)hypothesis test in which rejection region is only in the lower tail of the sampling distribution
D)hypothesis test in which rejection region is only in the upper tail of the sampling distribution

Question 36

In hypothesis testing if the null hypothesis has been rejected when the alternative hypothesis has been true,

A)a Type I error has been committed
B)a Type II error has been committed
C)either a Type I or Type II error has been committed
D)the correct decision has been made

Question 37

In hypothesis testing if the null hypothesis is rejected,

A)no conclusions can be drawn from the test
B)the alternative hypothesis must also be rejected
C)the data must have been accumulated incorrectly
D)None of the other answers are correct.

Question 38

A Type II error is committed when

A)a true alternative hypothesis is mistakenly rejected
B)a true null hypothesis is mistakenly rejected
C)the sample size has been too small
D)not enough information has been available

Question 39

The probability of making a Type I error is denoted by

A) $\alpha$
B) $\beta$
C)1 - $\alpha$
D)1 - $\beta$

Question 40

The level of significance can be any

A)negative value
B)value
C)value larger than 0.1
D)None of the answers is correct.

Question 41

Which of the following does not need to be known in order to compute the p-value?

A)knowledge of whether the test is one-tailed or two-tailed
B)the value of the test statistic
C)the level of significance
D)All of these are needed.

Question 42

A two-tailed test is performed at a 5% level of significance. The p-value is determined to be 0.09. The null hypothesis

A)must be rejected
B)should not be rejected
C)may or may not be rejected, depending on the sample size
D)has been designed incorrectly

Question 43

When using Excel to calculate a p-value for an upper-tail hypothesis test, the following must be used

A)RAND
B)1 - NORM.S.DIST
C)NORM.S.DIST
D)Not enough information is given to answer this question.

Question 44

Read the t statistic from the table of t distributions and circle the correct answer. A one-tailed test (lower tail), a sample size of 10 at a .10 level of significance; t =

A)1.383
B)-1.372
C)-1.383
D)-2.821

Question 45

Which Excel function would not be appropriate to use when conducting a hypothesis test for a population proportion?

A)NORM.S.DIST
B)COUNTIF
C)STDEV
D)All are appropriate.

Question 46

Excel's __________ function can be used to calculate a p-value for a hypothesis test.

A)RAND
B)NORM.S.DIST
C)NORM.S.INV
D)Not enough information is given to answer this question.

Question 47

When the p-value is used for hypothesis testing, the null hypothesis is rejected if

A)p-value $\le$ $\alpha$
B) $\alpha$ $\lt$ p-value
C)p-value $\gt$$\alpha$
D)p-value = z

Question 48

If a hypothesis is rejected at a 5% level of significance, it

A)will always be rejected at the 1% level
B)will always be accepted at the 1% level
C)will never be tested at the 1% level
D)may be rejected or not rejected at the 1% level

Question 49

Exhibit 9-1

Refer to Exhibit 9-1. The test statistic equals

A)2.3
B)0.38
C)-2.3
D)-0.38

Question 50

If a hypothesis is not rejected at a 5% level of significance, it will

A)also not be rejected at the 1% level
B)always be rejected at the 1% level
C)sometimes be rejected at the 1% level
D)Not enough information is given to answer this question.

Question 51

For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test,

A)will result in the rejection region being smaller
B)will result in the rejection region being larger
C)would have no effect on the rejection region
D)Not enough information is given to answer this question.

Question 52

Exhibit 9-1

Refer to Exhibit 9-1. The p-value is

A)0.5107
B)0.0214
C)0.0107
D)2.1

Question 53

In the past, 75% of the tourists who visited Chattanooga went to see Rock City. The management of Rock City recently undertook an extensive promotional campaign. They are interested in determining whether the promotional campaign actually increased the proportion of tourists visiting Rock City. The correct set of hypotheses is

A)H₀: p > 0.75 H_a: p $\le$ 0.75
B)H₀: p < 0.75 H_a: p $\ge$ 0.75
C)H₀: p $\ge$ 0.75 H_a: p < 0.75
D)H₀: p $\le$ 0.75 H_a: p > 0.75

Question 54

Read the t statistic from the table of t distributions and circle the correct answer. A two-tailed test, a sample of 20 at a .20 level of significance; t =

A)1.328
B)2.539
C)1.325
D)2.528

Question 55

The academic planner of a university thinks that at least 35% of the entire student body attends summer school. The correct set of hypotheses to test his belief is

A)H₀: p > 0.35 H_a: p $\ge$ 0.35
B)H₀: p $\le$ 0.35 H_a: p > 0.35
C)H₀: p $\ge$ 0.35 H_a: p < 0.35
D)H₀: p > 0.35 H_a: p $\le$ 0.35

Question 56

When using Excel to calculate a p-value for a lower-tail hypothesis test, the following must be used

A)RAND
B)1 - NORM.S.DIST
C)NORM.S.DIST
D)Not enough information is given to answer this question.

Question 57

The school's newspaper reported that the proportion of students majoring in business is at least 30%. You plan on taking a sample to test the newspaper's claim. The correct set of hypotheses is

A)H₀: p < 0.30 H_a: p $\ge$ 0.30
B)H₀: p $\le$ 0.30 H_a: p > 0.30
C)H₀: p $\ge$ 0.30 H_a: p < 0.30
D)H₀: p > 0.30 H_a: p $\le$ 0.30

Question 58

A p-value is the

A)probability, when the null hypothesis is true, of obtaining a sample result that is at least as unlikely as what is observed
B)value of the test statistic
C)probability of a Type II error
D)probability corresponding to the critical value(s) in a hypothesis test

Question 59

Excel's __________ function can be used to calculate a p-value for a hypothesis test when $\sigma$ is unknown.

A)RAND
B)T.DIST
C)NORM.S.DIST
D)Not enough information is given to answer this question.

Question 60

Read the t statistic from the table of t distributions and circle the correct answer. A one-tailed test (upper tail), a sample size of 18 at a .05 level of significance t =

A)2.12
B)1.734
C)-1.740
D)1.740

Question 61

Exhibit 9-2
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.
Refer to Exhibit 9-2. At a .05 level of significance, it can be concluded that the mean of the population is

A)significantly greater than 3
B)not significantly greater than 3
C)significantly less than 3
D)significantly greater then 3.18

Question 62

In a two-tailed hypothesis test, the null hypothesis should be rejected if the p-value is

A)less than or equal to $\alpha$
B)less than or equal to 2 $\alpha$
C)greater than or equal to $\alpha$
D)greater than or equal to 2 $\alpha$

Question 63

Exhibit 9-5
Assume population is normally distributed.
Refer to Exhibit 9-5. The p-value is equal to

A)-0.0166
B)0.0166
C)0.0332
D)0.9834

Question 64

For a two-tailed hypothesis test about a population mean, the null hypothesis can be rejected if the confidence interval

A)is symmetric
B)is non-symmetric
C)includes $\mu$ ₀
D)does not include $\mu$ ₀

Question 65

Exhibit 9-3

Refer to Exhibit 9-3. If the test is done at a 5% level of significance, the null hypothesis should

A)not be rejected
B)be rejected
C)Not enough information given to answer this question.
D)None of the other answers are correct.

Question 66

If a hypothesis test has a Type I error probability of .05, that means

A)if the null hypothesis is false, it will not be rejected 5% of the time
B)if the null hypothesis is false, it will be rejected 5% of the time
C)if the null hypothesis is true, it will not be rejected 5% of the time
D)if the null hypothesis is true, it will be rejected 5% of the time

Question 67

Exhibit 9-6
A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%.
Refer to Exhibit 9-6. At a .05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is

A)significantly greater than 75%
B)not significantly greater than 75%
C)significantly greater than 80%
D)not significantly greater than 80%

Question 68

Exhibit 9-3

Refer to Exhibit 9-3. The p-value is equal to

A)0.1151
B)0.3849
C)0.2698
D)0.2302

Question 69

Exhibit 9-3

Refer to Exhibit 9-3. The test statistic equals

A)0.1714
B)0.3849
C)-1.2
D)1.2

Question 70

Exhibit 9-2
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.
Refer to Exhibit 9-2. The p-value is

A)0.025
B)0.0456
C)0.05
D)0.0228

Question 71

Exhibit 9-4
A random sample of 16 students selected from the student body of a large university had an average age of 25 years. We want to determine if the average age of all the students at the university is significantly different from 24. Assume the distribution of the population of ages is normal with a standard deviation of 2 years.
Refer to Exhibit 9-4. At a .05 level of significance, it can be concluded that the mean age is

A)not significantly different from 24
B)significantly different from 24
C)significantly less than 24
D)significantly less than 25

Question 72

Exhibit 9-6
A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%.
Refer to Exhibit 9-6. The p-value is

A)0.2112
B)0.05
C)0.025
D)0.0156

Question 73

Exhibit 9-6
A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%.
Refer to Exhibit 9-6. The test statistic is

A)0.80
B)0.05
C)1.25
D)2.00

Question 74

Exhibit 9-4
A random sample of 16 students selected from the student body of a large university had an average age of 25 years. We want to determine if the average age of all the students at the university is significantly different from 24. Assume the distribution of the population of ages is normal with a standard deviation of 2 years.
Refer to Exhibit 9-4. The test statistic is

A)1.96
B)2.00
C)1.645
D)0.05

Question 75

Exhibit 9-2
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.
Refer to Exhibit 9-2. The test statistic is

A)1.96
B)1.64
C)2.00
D)0.056

Question 76

Exhibit 9-5
Assume population is normally distributed.
Refer to Exhibit 9-5. The test statistic equals

A)-2.131
B)-0.53
C)0.53
D)2.131

Question 77

The rejection region for a one-tailed hypothesis test

A)has an area of 1 - $\alpha$
B)has an area equal to the confidence coefficient
C)is in the tail that supports the null hypothesis
D)is in the tail that supports the alternative hypothesis

Question 78

Exhibit 9-1

Refer to Exhibit 9-1. If the test is done at a .05 level of significance, the null hypothesis should

A)not be rejected
B)be rejected
C)Not enough information is given to answer this question.
D)None of the other answers are correct.

Question 79

Exhibit 9-5
Assume population is normally distributed.
Refer to Exhibit 9-5. If the test is done at a 2% level of significance, the null hypothesis should

A)not be rejected
B)be rejected
C)Not enough information is given to answer this question.
D)None of the other answers are correct.

Question 80

For a two-tailed hypothesis test with a test statistic value of z = 2.05, the p-value is

A).0101
B).0202
C).0404
D).4899