Deck 13: Hypothesis Testing: Describing a Single Population

Question 1

Statisticians can translate p-values into several descriptive terms. Which of the following statements is correct?

A) If p-value < 0.01, there is overwhelming evidence to infer that the alternative hypothesis is true.
B) If 0.01 < p-value < 0.05, there is strong evidence to infer that the alternative hypothesis is true.
C) If 0.05 < p-value < 0.10, there is weak evidence to infer that the alternative hypothesis is true.
D) All of the above statements are correct.

Answer 1

D

Question 2

If a hypothesis is rejected at the 0.025 level of significance, it:

A) must be rejected at any level.
B) must be rejected at the 0.01 level.
C) must not be rejected at the 0.01 level.
D) may be rejected or not rejected at the 0.01 level.

Answer 2

D

Question 3

Which of the following p-values will lead us to reject the null hypothesis if the level of significance equals 0.10?

A) 0.001.
B) 0.01.
C) 0.05.
D) All of these choices are correct.

Answer 3

D

Question 4

For a two-tail Z test, the null hypothesis will be rejected at the 0.05 level of significance if the value of the standardised test statistic is:

A) smaller than -1.645.
B) greater than 1.96.
C) smaller than -1.645 or greater than 1.645.
D) smaller than -1.96 or greater than 1.96.

Question 5

The critical values z or z are the boundary values for the:

A) rejection region(s).
B) level of significance.
C) power of the test.
D) Type II error.

Question 6

In a two-tail test for the population mean, the null hypothesis will be rejected at the level of significance if the value of the standardised test statistic z is such that:

A) z > z .
B) z < -z .
C) -z < z < z .
D) |z| > z .

Question 7

A Type II error is committed if we make:

A) a correct decision when the null hypothesis is false.
B) correct decision when the null hypothesis is true.
C) incorrect decision when the null hypothesis is false.
D) incorrect decision when the null hypothesis is true.

Question 8

If a hypothesis is not rejected at the 0.10 level of significance, it:

A) must be rejected at the 0.05 level.
B) may be rejected at the 0.05 level.
C) will not be rejected at the 0.05 level.
D) must be rejected at the 0.025 level.

Question 9

In testing the hypotheses: 500 500, if the value of the Z test statistic equals 2.03, then the p-value is:

A) 0.0424.
B) 0.4788.
C) 0.9576.
D) 0.0212.

Question 10

In testing the hypotheses 75. < 75. if the value of the Z test statistic equals 1.78, then the p-value is:

A) 0.0.375.
B) 0.4625.
C) 0.9625.
D) 0.5375.

Question 11

Using the confidence interval when conducting a two-tail test for the population mean we do not reject the null hypothesis if the hypothesised value for :

A) is to the left of the lower confidence limit (LCL).
B) is to the right of the upper confidence limit (UCL).
C) falls between the LCL and UCL.
D) falls in the rejection region.

Question 12

The power of a test is the probability of making:

A) a correct decision when the null hypothesis is false.
B) a correct decision when the null hypothesis is true.
C) an incorrect decision when the null hypothesis is false.
D) an incorrect decision when the null hypothesis is true.

Question 13

A Type I error is committed if we make:

A) a correct decision when the null hypothesis is false.
B) correct decision when the null hypothesis is true.
C) incorrect decision when the null hypothesis is false.
D) incorrect decision when the null hypothesis is true.

Question 14

If the research question is not an equality statement, then in hypothesis testing it is specified as:

A) the null hypothesis.
B) either the null or the alternative hypothesis.
C) the alternative hypothesis.
D) the test statistic.

Question 15

In order to determine the p-value, which of the following items of information is not needed?

A) The level of significance.
B) Whether the test is one- or two-tailed.
C) The value of the test statistic.
D) All of the above are needed.

Question 16

Suppose that we reject a null hypothesis at the 0.05 level of significance. For which of the following -values do we also reject the null hypothesis?

A) 0.06.
B) 0.04.
C) 0.03.
D) 0.02.

Question 17

In a one-tail test for the population mean, if the null hypothesis is not rejected when the alternative hypothesis is true:

A) a Type I error is committed.
B) a Type II error is committed.
C) a correct decision is made.
D) a two-tail test should be used instead of a one-tail test.

Question 18

In testing the hypotheses: $H _ { 0 } : \mu =$ 35 H₁ : $\mu$ < 35,
The following information is known: n = 49, $\bar { x }$ = 37 and $\sigma$ = 16. The standardised test statistic equals:

A) 0.33.
B) -0.33.
C) -2.33.
D) 2.33.

Question 19

In testing the hypotheses H₀ : $\mu$ = 75.
H₁ : $\mu$ < 75.
The p-value is found to be 0.042, and the sample mean is 80. Which of the following statements is true?

A) The probability of observing a sample mean at most as large as 75 from a population whose mean is 100 is 0.042.
B) The smallest value of $\alpha$ that would lead to the rejection of the null hypothesis is 0.042.
C) The probability that the population mean is smaller than 75 is 0.042.
D) None of the above statements is correct.

Question 20

In a two-tail test for the population mean, if the null hypothesis is rejected when the alternative hypothesis is false:

A) a Type I error is committed.
B) a Type II error is committed.
C) a correct decision is made.
D) a one-tail test should be used instead of a two-tail test.

Question 21

In a one-tail test, the p-value is found to be equal to 0.032. If the test had been two-tailed, the p-value would have been:

A) 0.064.
B) 0.080.
C) 0.016.
D) 0.066.

Question 22

A Type II error is defined as:

A) rejecting a true null hypothesis.
B) rejecting a false null hypothesis.
C) not rejecting a true null hypothesis.
D) not rejecting a false null hypothesis.

Question 23

The power of a test is the probability that it will lead us to:

A) reject the null hypothesis when it is true.
B) reject the null hypothesis when it is false.
C) fail to reject the null hypothesis when it is true.
D) fail to reject the null hypothesis when it is false.

Question 24

In a given hypothesis test, the null hypothesis can be rejected at the 0.10 level of significance, but cannot be rejected at the 0.05 and 0.01 levels. The most accurate statement about the p-value for this test is:

A) p-value > 0.01.
B) 0.05 < p-value < 0.10.
C) 0.01 < p-value < 0.10.
D) 0.01 < p-value < 0.05.

Question 25

Which of the following best describes the p-value of a test?

A) The p-value is the probability of getting our statistical table value of the test statistic if the null hypothesized value of the population parameter, were really true.
B) The p-value is the probability of getting our calculated test statistic or more extreme if the null hypothesized value of the population parameter, were really true.
C) The p-value is the probability of getting our calculated test statistic, or more extreme, if the null hypothesized value of the population parameter, were really false.
D) None of these choices are correct.

Question 26

The confidence interval approach can be employed to conduct tests of hypotheses. Which of the following statements is false?

A) The confidence interval approach is equivalent to the rejection region approach.
B) The confidence interval approach has the disadvantage of complexity.
C) One-sided confidence intervals can be used when conducting a one-tail test.
D) The confidence interval approach does not yield a p-value.

Question 27

In a criminal trial, a Type II error is made when:

A) a guilty defendant is acquitted.
B) an innocent person is convicted.
C) a guilty defendant is convicted.
D) an innocent person is acquitted.

Question 28

The power of a test is denoted by:

A) .
B) .
C) 1 - .
D) 1 - .

Question 29

The probability of a Type I error is denoted by:

A) .
B) 1 - .
C) .
D) 1 - .

Question 30

Whenever the null hypothesis is not rejected:

A) the null hypothesis is true.
B) the alternative hypothesis is false.
C) the null hypothesis is maintained.
D) the null hypothesis is accepted.

Question 31

A spouse stated that the average amount of money spent on Christmas gifts for immediate family members is above $1200. The correct set of hypotheses is:

A) . .
B) . .
C) . .
D) . .

Question 32

If we reject the null hypothesis, we conclude that:

A) there is enough statistical evidence to infer that the alternative hypothesis is true.
B) there is not enough statistical evidence to infer that the alternative hypothesis is true.
C) there is enough statistical evidence to infer that the null hypothesis is true.
D) the test is statistically insignificant at whatever level of significance the test was conducted at.

Question 33

We cannot commit a Type I error when the:

A) null hypothesis is true.
B) level of significance is 0.10.
C) null hypothesis is false.
D) test is a two-tail test.

Question 34

The probability of a Type II error is denoted by:

A) .
B) .
C) 1 - .
D) 1 - .

Question 35

In a criminal trial, a Type I error is made when:

A) a guilty defendant is acquitted.
B) an innocent person is convicted.
C) a guilty defendant is convicted.
D) an innocent person is acquitted.

Question 36

If we do not reject the null hypothesis, we conclude that:

A) there is enough statistical evidence to infer that the alternative hypothesis is true.
B) there is not enough statistical evidence to infer that the alternative hypothesis is true.
C) there is enough statistical evidence to infer that the null hypothesis is true.
D) the test is statistically insignificant at whatever level of significance the test was conducted at.

Question 37

For a given level of significance, if the sample size decreases, the probability of a Type II error will:

A) remain the same.
B) increase.
C) decrease.
D) be equal to 1.0 regardless of the value of .

Question 38

Which of the following statements is (are) not true?

A) The probability of making a Type II error increases as the probability of making a Type I error decreases.
B) The probability of making a Type II error and the level of significance are the same.
C) The power of the test decreases as the level of significance decreases.
D) None of the above statements are true.

Question 39

A Type I error occurs when we:

A) reject a false null hypothesis.
B) reject a true null hypothesis.
C) don't reject a false null hypothesis.
D) don't reject a true null hypothesis.

Question 40

If the value of the sample mean is close enough to the hypothesised value of the population mean , then:

A) the hypothesised value is definitely true.
B) the hypothesised value is definitely false.
C) we reject the null hypothesis.
D) we don't reject the null hypothesis.

Question 41

In any given test, it is possible to commit the Type I and Type II errors at the same time.

Question 42

Which of the following test statistics may be used to test a value of the population proportion?

A) Z test or a t test
B) t test
C) Z test
D) None of these choices are correct

Question 43

The critical values will bound the rejection and non-rejection regions for the null hypothesis.

Question 44

The rejection region for testing the hypotheses 80. < 80. at the 0.10 level of significance is:

A) z > 1.96.
B) z < 0.90.
C) z > -1.65.
D) z < -1.28.

Question 45

The power of a test is the probability that a true null hypothesis will be rejected.

Question 46

A Type I error is represented by , and is the probability of not rejecting a false null hypothesis.

Question 47

The p-value of a test is the probability of observing a test statistic at least as extreme as the one computed, given that the null hypothesis is true.

Question 48

Reducing the probability of a Type I error, increases the probability of a Type II error.

Question 49

The p-value criterion for hypothesis testing is to retain the null hypothesis if:

A) p-value = .
B) p-value < .
C) p-value > .
D) - < p-value < .

Question 50

The rejection region for testing the hypotheses 100. 100. at the 0.05 level of significance is:

A) |z| < 0.95.
B) |z| > 1.96.
C) z > 1.65.
D) z < 2.33.

Question 51

A one-tail p-value is two times the size of that for a two-tail test.

Question 52

The power of a test refers to the probability of rejecting a false null hypothesis.

Question 53

In any test, the probability of a Type I error and the probability of a Type II error add up to 1.

Question 54

An alternative or research hypothesis is an assertion that holds if the null hypothesis is false.

Question 55

Which of the following statements best describes the level of significance?

A) The smaller the level of significance, the larger the rejection region, so therefore the tighter the test.
B) The larger the level of significance, the smaller the rejection region, so therefore the tighter the test.
C) The smaller the level of significance, the smaller the rejection region, so therefore the tighter the test.
D) None of these choices are correct

Question 56

A null hypothesis is a statement about the value of a population parameter; it is put up for testing in the face of numerical evidence.

Question 57

The p-value is usually 0.05.

Question 58

A two-tail test is a test in which a null hypothesis can be rejected by an extreme result occurring in either direction.

Question 59

When testing whether the majority of voters in an electorate will vote for a particular candidate, which of the following sets of hypotheses are correct?

A) Ho: p = 0.50
H_A: p < 0.50
B) Ho: p > 0.50
H_A: p = 0.50
C) Ho: p = 0.50
H_A: p > 0.50
D) None of these choices are correct

Question 60

A Type I error is represented by , and is the probability of incorrectly rejecting a true null hypothesis.

Question 61

The p-value of a test is the smallest value of at which the null hypothesis can be rejected.

Question 62

A two-tail test for the population mean produces a test-statistic z = -1.43. The p-value associated with the test is 0.0764.

Question 63

Using the confidence interval when conducting a two-tail test for the population mean , we do not reject the null hypothesis if the hypothesised value for is smaller than the upper confidence limit.

Question 64

In order to determine the p-value, it is not necessary to know the level of significance.

Question 65

The probability of making a Type I error and the level of significance are the same.

Question 66

In a one-tail test, the p-value is found to be equal to 0.018. If the test had been two-tailed, the p-value would have been 0.036.

Question 67

A Type II error is represented by and is the probability of failing to reject a false null hypothesis.

Question 68

In a two-tail test for the population mean, if the null hypothesis is rejected when the alternative hypothesis is true, a Type I error is committed.

Question 69

There is a direct relationship between the power of a test and the probability of a Type II error.

Question 70

There is an inverse relationship between the probabilities of Type I and Type II errors.

Question 71

A test for the population mean produces a test-statistic z = -0.75. The p-value associated with the test is 0.2266 if the test is a left-tail test, it is 0.7734 if the test is a right-tail test, and it is 0.4533 if the test is a two-tail test.

Question 72

If we do not reject the null hypothesis, we conclude that there is enough statistical evidence to infer that the null hypothesis is true.

Question 73

If a null hypothesis is rejected at the 0.05 level of significance, it cannot be rejected at the 0.10 level.

Question 74

In a criminal trial, a Type II error is made when an innocent person is acquitted.

Question 75

A professor of statistics refutes the claim that the average student spends 6 hours studying for the final. To test the claim, the hypotheses H₀: $\mu$ = 6, H₁: $\mu$ < 6 should be used.

Question 76

In a criminal trial, a Type I error is made when an innocent person is convicted.

Question 77

A Type I error is represented by , and is the probability of rejecting a true null hypothesis.

Question 78

If we reject the null hypothesis, we conclude that there is enough statistical evidence to infer that the alternative hypothesis is true.

Question 79

If we reject a null hypothesis at the 0.05 level of significance, then we must also reject it at the 0.10 level.

Question 80

In a one-tail test for the population mean, if the null hypothesis is not rejected when the alternative hypothesis is true, a Type I error is committed.