Deck 12: Hypothesis Testing: Describing a Single Population

Question 1

In testing the hypotheses: H0:  = 500
HA:  = 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.

Answer 1

0.0424.

Question 2

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.

Answer 2

will not be rejected at the 0.05 level.

Question 3

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

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.

Answer 3

falls between the LCL and UCL.

Question 4

In testing the hypotheses H0:  = 75
HA:  < 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 5

The critical values zα or zα/2 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 testing the hypotheses: H0: ? = 35
HA: ? < 35,
The following information is known: n = 49, $\bar { X }$ = 37 and $\sigma$ = 6. The standardised test statistic equals:

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

Question 7

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.

Question 8

Suppose you intend to test the claim that a typical high school student in Sydney spends more than $50 a week on mobile phone calls. Which hypotheses are used to test the claim?

A)H0:   50.HA:  < 50.
B)H0:  = 50.HA:   50.
C)H0:   50.HA:  = 50.
D)H0:  = 50.HA:  > 50.

Question 9

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 10

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.

Question 11

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

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

Question 12

In testing the hypotheses H0:  = 75.
HA:  < 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  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 13

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 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 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 16

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 17

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 18

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 19

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-tail.
C)The value of the test statistic.
D)All of the above are needed.

Question 20

In a two-tail test for the population mean, the null hypothesis will be rejected at the $\alpha$ 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 21

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 22

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 23

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

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

Question 24

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)H0:  = 1200 HA:  < 1200.
B)H0:  > 1200 HA:  =1200.
C)H0:  = 1200 HA:  > 1200.
D)H0:  < 1200 HA:  = 1200.

Question 25

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 26

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.

Question 27

The probability of a Type II error is denoted by:

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

Question 28

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 29

The rejection region for testing the hypotheses H0:  = 100
HA:  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 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

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 32

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 33

A Type I error occurs when we:

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

Question 34

The probability of a Type I error is denoted by:

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

Question 35

The power of a test is denoted by:

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

Question 36

If the value of the sample mean $\bar { X }$ 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 Do not reject the null hypothesis.

Question 37

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 38

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 39

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 40

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 $\alpha$ .

Question 41

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

Question 42

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

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

Question 43

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 44

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

Question 45

The rejection region for testing the hypotheses H0:  = 80
HA:  < 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 46

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

Question 47

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

Question 48

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 49

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

Question 50

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 51

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

Question 52

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 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

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

Question 55

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

Question 56

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

Question 57

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

Question 58

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

Question 59

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

Question 60

The p-value is usually 0.05.

Question 61

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 62

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

Question 63

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

Question 64

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 65

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 66

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:  = 6, HA:  < 6 should be used.

Question 67

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.

Question 68

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

Question 69

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 70

If a sample size is increased at a given $\alpha$ level, the probability of committing a Type I error increases.

Question 71

When testing a value of the population mean, if the population variance is unknown, then we must do a t-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

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

Question 74

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

Question 75

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

Question 76

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

Question 77

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

Question 78

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

Question 79

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

Question 80

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