Deck 9: Hypothesis Tests

Question 1

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.

Answer 1

maximum allowable probability of Type I error.

Question 2

If the null hypothesis is rejected in hypothesis testing,

A) no conclusions can be drawn from the test.
B) the alternative hypothesis is true.
C) the data must have been accumulated incorrectly.
D) the sample size has been too small.

Answer 2

the alternative hypothesis is true.

Question 3

The error of rejecting a true null hypothesis is

A) a Type I error.
B) a Type II error.
C) always negligible in hypothesis testing.
D) never committed in hypothesis testing.

Answer 3

a Type I error.

Question 4

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 a Type II error has been committed.
D) the correct decision has been made.

Question 5

The p-value is

A) the same as the z statistic.
B) a sample statistic.
C) a distance.
D) a probability.

Question 6

For a given sample size in hypothesis testing,

A) the smaller the Type I error, the smaller the Type II error will be.
B) the smaller the Type I error, the larger the Type II error will be.
C) Type II error will not be affected by Type I error.
D) the sum of Type I and Type II errors must equal to 1.

Question 7

For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic as

A) likely as that provided by the sample.
B) unlikely as that provided by the sample.
C) likely as that provided by the population.
D) unlikely as that provided by the population.

Question 8

The p-value is a probability that measures the support (or lack of support) for

A) the null hypothesis.
B) the alternative hypothesis.
C) either the null or the alternative hypothesis.
D) neither the null nor the alternative hypothesis.

Question 9

For a lower tail test, the p-value is the probability of obtaining a value for the test statistic at least as

A) small as that provided by the sample.
B) large as that provided by the sample.
C) small as that provided by the population.
D) large as that provided by the population.

Question 10

The probability of making a Type I error is denoted by

A) α.
B) β.
C) 1 - α.
D) 1 - β.

Question 11

The critical value of t for a two-tailed test with 10 degrees of freedom using α = .05 is

A) 1.833.
B) 1.812.
C) 2.262.
D) 2.228.

Question 12

The power curve provides the probability of

A) correctly accepting the null hypothesis.
B) incorrectly accepting the null hypothesis.
C) incorrectly rejecting the null hypothesis.
D) correctly rejecting the null hypothesis.

Question 13

What type of error occurs if you fail to reject H₀ when, in fact, it is not true?

A) Type II
B) Type I
C) either Type I or Type II, depending on the level of significance
D) either Type I or Type II, depending on whether the test is one-tailed or two-tailed

Question 14

The probability of committing a Type I error when the null hypothesis is true as an equality is

A) the confidence level.
B) β.
C) greater than 1.
D) the level of significance.

Question 15

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 true null hypothesis is correctly rejected.
D) the true alternative hypothesis is correctly rejected.

Question 16

In hypothesis testing, the tentative assumption about the population parameter is

A) the alternative hypothesis.
B) the null hypothesis.
C) either the null or the alternative.
D) neither the null nor the alternative.

Question 17

The p-value

A) can be any negative value.
B) can be any positive value.
C) must be a number between -1 and 0.
D) must be a number between zero and one.

Question 18

The level of significance, in hypothesis testing, is the probability of _____ null hypothesis.

A) accepting a true
B) accepting a false
C) rejecting a true
D) rejecting a false

Question 19

An assumption made about the value of a population parameter is called a(n)

A) hypothesis.
B) conclusion.
C) error.
D) probability.

Question 20

The sum of the values of α and β

A) is always 1.
B) is always .5.
C) gives the probability of taking the correct decision.
D) is not needed in hypothesis testing.

Question 21

In order to test the following hypotheses at an α level of significance ​
H₀: μ 800
H_a: μ > 800
​
The null hypothesis will be rejected, if the test statistic z is

A) zα.
B) < z_α.
C) < -z_α.
D) = α.

Question 22

If the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error will

A) also increase from .01 to .05.
B) not change.
C) decrease.
D) increase.

Question 23

Read the z statistic from the normal distribution table and choose the correct answer. For a two-tailed test using α = .0802, z =

A) .85.
B) 1.75.
C) 1.405.
D) .2.88.

Question 24

For a lower tail test, the test statistic z is determined to be zero. The p-value for this test is

A) zero.
B) -.5.
C) +.5.
D) 1.

Question 25

Read the z statistic from the normal distribution table and choose the correct answer. For a one-tailed test (upper tail) using α = .0721, z =

A) 1.54.
B) 1.96.
C) 1.645.
D) 1.46.

Question 26

Read the t statistic from the t distribution table and choose the correct answer. For a two-tailed test with a sample size of 20 and using α = .20, t =

A) 1.341.
B) 1.337.
C) .865.
D) .866.

Question 27

If the null hypothesis is rejected at the .05 level of significance, it will _____ be rejected at the .10 level of significance.

A) always not
B) always
C) sometimes
D) sometimes not

Question 28

If the probability of a Type I error (α) is .05, then the probability of a Type II error (β) must be

A) .05.
B) .95.
C) .025.
D) Cannot be computed.

Question 29

Read the z statistic from the normal distribution table and choose the correct answer. For a one-tailed test (lower tail) using α = .0901, z =

A) -1.86.
B) -1.34.
C) -1.96.
D) -1.645.

Question 30

If the null hypothesis is rejected at the 5% level of significance, it _____ at the 1% level.

A) will always be rejected
B) will always not be rejected
C) will never be tested
D) may be rejected or not rejected

Question 31

As the test statistic becomes larger, the p-value

A) gets smaller.
B) becomes larger.
C) goes beyond 1.
D) becomes negative.

Question 32

If a hypothesis test leads to the rejection of the null hypothesis, a _____ have been committed.

A) Type II error must
B) Type II error may
C) Type I error must
D) Type I error may

Question 33

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

A) p-value α.
B) α < p-value.
C) p-value = 1 - α/2.
D) p-value = 1 - α.

Question 34

In a two-tailed hypothesis test situation, the test statistic is determined to be t = -2.032. The sample size is 35. The p-value for this test is

A) -.05.
B) +.05.
C) -.10.
D) +.10.

Question 35

The probability of making a Type II error is denoted by

A) α.
B) β.
C) 1 - α.
D) 1 - β.

Question 36

In a lower tail hypothesis test situation, the p-value is determined to be .2. If the sample size for this test is 41, the t statistic has a value of

A) .851.
B) -.851.
C) 1.303.
D) -1.303.

Question 37

When the following hypotheses are being tested at a level of significance of α ​
H₀: μ 500
H_a: μ < 500
​
The null hypothesis will be rejected, if the p-value is

A) α.
B) > α.
C) = α/2.
D) 1 - α/2.

Question 38

In the hypothesis testing procedure, α is the

A) level of significance.
B) critical value.
C) confidence level.
D) p-value.

Question 39

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) The probability distribution of the test statistic

Question 40

If the null hypothesis is not rejected at the 5% level of significance, it _____ rejected at the 1% level.

A) will also not be
B) will always be
C) will sometimes be
D) may be rejected or not

Question 41

The average manufacturing work week in metropolitan Chattanooga was 40.2 hours last year. It is believed that the recession has led to a reduction in the average work week. To test the validity of this belief, the hypotheses are

A) H₀: μ < 40.2 H_a: μ ≥ 40.2.
B) H₀: μ ≥ 40.2 H_a: μ < 40.2.
C) H₀: μ > 40.2 H_a: μ ≤ 40.2.
D) H₀: μ = 40.2 H_a: μ ≠ 40.2.

Question 42

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 > .75 H_a: p .75.
B) H₀: p < .75 H_a: p .75.
C) H₀: p .75 H_a: p < .75.
D) H₀: p .75 H_a: p > .75.

Question 43

Read the z statistic from the normal distribution table and choose the correct answer. For a one-tailed test (lower tail) using α = .005, z =

A) -2.575.
B) -1.645.
C) 2.575.
D) 1.645.

Question 44

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 their tires has increased. In order to test the validity of their belief, the correct set of hypotheses is

A) H₀: μ < 40,000 H_a: μ 40,000.
B) H₀: μ 40,000 H_a: μ > 40,000.
C) H₀: μ > 40,000 H_a: μ 40,000.
D) H₀: μ 40,000 H_a: μ < 40,000.

Question 45

Read the z statistic from the normal distribution table and choose the correct answer. For a one-tailed test (upper tail) at α = .0630, z =

A) -1.53.
B) 0.335.
C) -0.335.
D) 1.53.

Question 46

Read the t statistic from the t distribution table and choose the correct answer. For a one-tailed test (upper tail), using a sample size of 14, and at the 5% level of significance, t =

A) 1.761.
B) -1.761.
C) -1.771.
D) 1.771.

Question 47

A two-tailed test is performed at the .05 level of significance. The p-value is determined to be .01. The null hypothesis

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

Question 48

In a one-tailed hypothesis test (lower tail), the test statistic is determined to be 2. The p-value for this test is

A) .9772.
B) .0228.
C) .0056.
D) .5228.

Question 49

A juice drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of drink on an average. 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: μ < 12 H_a: μ ≥ 12.
B) H₀: μ 12 H_a: μ > 12.
C) H₀: μ ≠ 12 H_a: μ = 12.
D) H₀: μ = 12 H_a: μ ≠ 12.

Question 50

A machine is designed to fill toothpaste tubes, on an average, with 5.8 ounces of toothpaste. The manufacturer does not want any underfilling or overfilling. The correct hypotheses to be tested are

A) H₀: μ ≠ 5.8 H_a: μ = 5.8.
B) H₀: μ = 5.8 H_a: μ ≠ 5.8.
C) H₀: μ > 5.8 H_a: μ ≤ 5.8.
D) H₀: μ ≥ 5.8 H_a: μ < 5.8.

Question 51

Read the t statistic from the t distribution table and choose the correct answer. For a one-tailed test (upper tail) with a sample size of 16 and at the .10 level, t =

A) 1.341.
B) -1.341.
C) -1.753.
D) 1.753.

Question 52

The average monthly rent for one-bedroom apartments in Chattanooga has been $800. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are

A) H₀: μ ≥ 800 H_a: μ < 800.
B) H₀: μ = 800 H_a: μ ≠ 800.
C) H₀: μ > 800 H_a: μ ≤ 800.
D) H₀: μ < 800 H_a: μ ≥ 800.

Question 53

Read the t statistic from the t distribution table and choose the correct answer. For a one-tailed test (lower tail), using a sample size of 14, and at the 5% level of significance, t =

A) 1.771.
B) 1.761.
C) -1.771.
D) -1.762.

Question 54

For a one-tailed hypothesis test (upper tail), the p-value is computed to be .034. If the test is being conducted at the 1% level of significance, the null hypothesis

A) could be rejected or not rejected depending on the sample size.
B) could be rejected or not rejected depending on the sample mean.
C) is not rejected.
D) is rejected.

Question 55

The average hourly wage of computer programmers with 2 years of experience has been $21.80. Because of high demand for computer programmers, it is believed there has been a significant increase in the average hourly wage of computer programmers. To test whether or not there has been an increase, the correct hypotheses to be tested are

A) H₀: μ < 21.80 H_a: μ ≥ 21.80.
B) H₀: μ = 21.80 H_a: μ ≠ 21.80.
C) H₀: μ > 21.80 H_a: μ ≤ 21.80.
D) H₀: μ ≤ 21.80 H_a: μ > 21.80.

Question 56

Read the z statistic from the normal distribution table and choose the correct answer. For a two-tailed test using α = .0150, z =

A) 1.96.
B) 2.17.
C) -2.17.
D) -125.

Question 57

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 < .35 H_a: p .35.
B) H₀: p .35 H_a: p > .35.
C) H₀: p .35 H_a: p < .35.
D) H₀: p > .35 H_a: p .35.

Question 58

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: μ < 85 H_a: μ 85.
B) H₀: μ 85 H_a: μ > 85.
C) H₀: μ 85 H_a: μ < 85.
D) H₀: μ > 85 H_a: μ 85.

Question 59

Read the t statistic from the t distribution table and circle the correct answer. For a one-tailed test (lower tail) with 22 degrees of freedom at α = .05, the value of t =

A) 1.717.
B) 1.721.
C) -1.717.
D) -1.721.

Question 60

In a two-tailed hypothesis test, the test statistic is determined to be z = 2.5. The p-value for this test is

A) .9876.
B) .4938.
C) .0062.
D) .0124.

Question 61

A random sample of 100 people was taken. Eighty-five 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 80%. The p-value is

A) .2112.
B) .05.
C) .025.
D) .1056.

Question 62

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 63

For the following hypothesis test, H₀: μ ≥ 150
H_a: μ < 150
​
The test statistic

A) must be negative.
B) must be positive.
C) can be either negative or positive.
D) must be a number between zero and one.

Question 64

A 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 < .30 H_a: p .30.
B) H₀: p .30 H_a: p > .30.
C) H₀: p .30 H_a: p < .30.
D) H₀: p > .30 H_a: p .30.

Question 65

A random sample of 100 people was taken. Eighty-five 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 80%. At the .05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is

A) significantly greater than 80%.
B) not significantly greater than 80%.
C) significantly greater than 85%.
D) not significantly greater than 85%.

Question 66

A grocery store has an average sales of $8000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 100 days of sales was selected. It was found that the average was $8200 per day. From past information, it is known that the standard deviation of the population is $1500. The correct null hypothesis for this problem is

A) μ ≤ 8000.
B) μ ≤ 8200.
C) μ = 8000.
D) μ > 8200.

Question 67

A grocery store has an average sales of $8000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 100 days of sales was selected. It was found that the average was $8200 per day. From past information, it is known that the standard deviation of the population is $1500. The p-value is

A) 1.3333.
B) .9082.
C) .0918.
D) .1333.

Question 68

A weatherman stated that the average temperature during July in Chattanooga is 80 degrees or less. A sample of 32 Julys is taken to test the weatherman's statement. The correct set of hypotheses is

A) H₀: μ 80 H_a: μ < 80.
B) H₀: μ 80 H_a: μ > 80.
C) H₀: μ ≠ 80 H_a: μ = 80.
D) H₀: μ < 80 H_a: μ > 80.

Question 69

More evidence against H₀ is indicated by​

A) ​lower levels of significance.
B) ​smaller p-values.
C) ​smaller critical values.
D) lower probabilities for the power of the test.

Question 70

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: μ < 10.0% H_a: μ 10.0%.
B) H₀: μ 10.0% H_a: μ > 10.0%.
C) H₀: μ > 10.0% H_a: μ 10.0%.
D) H₀: μ 10.0% H_a: μ < 10.0%.

Question 71

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 72

A sample of 1400 items had 280 defective items. For the following hypothesis test, ​
H₀: p ≤ .20
H_a: p > .20
​
The test statistic is

A) .28.
B) .14.
C) .20.
D) zero.

Question 73

A random sample of 25 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. Using α = .05, it can be concluded that the population mean age is

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

Question 74

A random sample of 25 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. The p-value is between

A) .005 to .01.
B) .01 to .025.
C) .025 to .05.
D) .05 to .10.

Question 75

Given the following information, ​
N = 36, = 60, s =12
H₀: μ ≥ 63
H_a: μ < 63
​
The test statistic is

A) .67.
B) -67.
C) 1.5.
D) -1.5.

Question 76

A grocery store has an average sales of $8000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 100 days of sales was selected. It was found that the average was $8200 per day. From past information, it is known that the standard deviation of the population is $1500. The value of the test statistic is

A) .013.
B) .133.
C) 13.33.
D) 1.33.

Question 77

A random sample of 25 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. The test statistic is

A) 1.96.
B) 2.50.
C) 1.65.
D) .05.

Question 78

A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether the proportion of the population in favor of Candidate A is significantly more than 75%. The test statistic is

A) .8.
B) .75.
C) 1.15.
D) -1.25.

Question 79

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

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

Question 80

The manager of a laptop computer dealership is considering a new bonus plan in order to increase sales. Currently, the mean sales rate per salesperson is five laptops per week. The correct set of hypotheses for testing the effect of the bonus plan is

A) H₀: μ < 5 H_a: μ ≥ 5.
B) H₀: μ 5 H_a: μ > 5.
C) H₀: μ > 5 H_a: μ 5.
D) H₀: μ 5 H_a: μ < 5.