Deck 13: Hypothesis Testing: Describing a Single Population

Question 1

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

Answer 1

D

Question 2

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?

Answer 2

A

Question 3

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

Answer 3

A

Question 4

A Type II error is committed if we make: $\begin{array}{|l|l|}\hline A.&\text { a correct decision when the null hypothesis is false. }\\\hline B.&\text {correct decision when the null hypothesis is true. }\\\hline C.&\text { incorrect decision when the null hypothesis is false. }\\\hline D.&\text { incorrect decision when the null hypothesis is true.}\\\hline \end{array}$

Question 5

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:

Question 6

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:

Question 7

In a one-tail test for the population mean, if the null hypothesis is not rejected when the alternative hypothesis is true: $\begin{array}{|l|l|}\hline A.&\text { a Type I error is committed.}\\\hline B.&\text {a Type II error is committed. }\\\hline C.&\text {a correct decision is made. }\\\hline D.&\text { a two-tail test should be used instead of a one-tail test.}\\\hline \end{array}$

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

The critical values z $\mathrm{\alpha}$ or z $\alpha / 2$ are the boundary values for the: $\begin{array}{|l|l|}\hline A.&\text { rejection region(s). } \\\hline B.&\text { level of significance. } \\\hline C. &\text { power of the test. } \\\hline D.& \text { Type II error. } \\\hline \end{array}$

Question 13

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: $\begin{array}{|l|l|}\hline \text { A. } & 0.33 . \\\hline \text { B. } & -0.33 \\\hline \text { C. } & -2.33 \\\hline \text { D. } & 2.33 . \\\hline\end{array}$

Question 14

In a two-tail test for the population mean, if the null hypothesis is rejected when the alternative hypothesis is false: $\begin{array}{|l|l|}\hline A.&\text { a Type I error is committed.}\\\hline B.&\text {a Type II error is committed. }\\\hline C.&\text {a correct decision is made. }\\\hline D.&\text { a one-tail test should be used instead of a two-tail test.}\\\hline \end{array}$

Question 15

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?

Question 16

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

Question 17

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 18

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 :

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? $\begin{array}{|l|l|}\hline A.&\text {The probability of observing a sample mean at most as large as 75 from a population }\\&\text { whose mean is 100 is 0.042 }\\\hline B.&\text {The smallest value of \( \alpha \) that would lead to the rejection of the null hypothesis is 0.042 . }\\\hline C.&\text {The probability that the population mean is smaller than 75 is 0.042 . }\\\hline D.&\text {None of the above statements is correct. }\\\hline \end{array}$

Question 20

A Type I error is committed if we make: $\begin{array}{|l|l|}\hline A.&\text { a correct decision when the null hypothesis is false. }\\\hline B.&\text {correct decision when the null hypothesis is true. }\\\hline C.&\text { incorrect decision when the null hypothesis is false. }\\\hline D.&\text { incorrect decision when the null hypothesis is true.}\\\hline \end{array}$

Question 21

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

Question 22

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

Question 23

A Type II error is defined as: $\begin{array}{|l|l|}\hline A.&\text {rejecting a true null hypothesis. }\\\hline B.&\text {rejecting a fal se null hypothesis. }\\\hline C.&\text { not rejecting a true null hypothesis. }\\\hline D.&\text {not rejecting a false null hypothesis. }\\\hline \end{array}$

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:

Question 25

Whenever the null hypothesis is not rejected: $\begin{array}{|l|l|}\hline A.&\text {the null hypothesis is true. }\\\hline B.&\text { the alternative hypothesis is false.}\\\hline C.&\text { the null hypothesis is maintained.}\\\hline D.&\text {the null hypothesis is accepted. }\\\hline \end{array}$

Question 26

A Type I error occurs when we: $\begin{array}{|l|l|}\hline A.&\text { reject a false null hypothesis.}\\\hline B.&\text { eject a true null hypothesis.}\\\hline C.&\text {don't reject a false null hypothesis. }\\\hline D.&\text { don't reject a true null hypothesis.}\\\hline \end{array}$

Question 27

The probability of a Type II error is denoted by:

Question 28

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

Question 29

If we reject the null hypothesis, we conclude that: $\begin{array}{|l|l|}\hline \text { A. } & \text { there is enough statistical evidence to infer that the alternative hypothesis is true. } \\\hline \text { B. } & \text { there is not enough statistical evidence to infer that the al ternative hypothesis is true. } \\\hline \text { C. } & \text { there is enough statistical evidence to infer that the null hypothesis is true. } \\\hline \text { D. } & \text { the test is statistically insignificant at whatever level of significance the test was conducted } \\&\text { at. }\\\hline \end{array}$

Question 30

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:

Question 31

Statisticians can translate p-values into several descriptive terms. Which of the following statements is correct? $\begin{array}{|l|l|}\hline A.&\text {If \( p \)-value \( <0.01 \), there is overwhelming evidence to infer that the al ternative }\\&\text {hypothesis is true. }\\\hline B.&\text {If \( 0.01< p \)-value \( <0.05 \), there is strong evidence to infer that the alternative }\\&\text {hypothesis is true. }\\\hline C.&\text { If \( 0.05< p \)-value \( <0.10 \), there is weak evidence to infer that the alternative}\\&\text {hypothesis is true. }\\\hline D.&\text {All of the above statements are correct. }\\\hline \end{array}$

Question 32

The probability of a Type I error is denoted by:

Question 33

Which of the following statements is (are) not true? $\begin{array}{|l|l|}\hline A&\text { The probability of making a Type II error increases as the probability of making a Type I } \\&\text { error decreases. } \\\hline B&\text { The probability of making a Type II error and the level of significance are the same. } \\\hline C&\text { The power of the test decreases as the level of signi ficance decreases. } \\\hline D&\text { None of the above statements are true. }\\\hline \end{array}$

Question 34

The power of a test is the probability that it will lead us to: $\begin{array}{|l|l|}\hline A.&\text {reject the null hypothesis when it is true. }\\\hline B.&\text {reject the null hypothesis when it is false. }\\\hline C.&\text {fail to reject the null hypothesis when it is true. }\\\hline D.&\text { fail to reject the null hypothesis when it is false. }\\\hline \end{array}$

Question 35

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:

Question 36

If the value of the sample mean $\bar { x }$ is close enough to the hypothesised value of the population mean $\mu$ , then: $\begin{array}{|l|l|}\hline A&\text { the hypothesised value is definitely true.}\\\hline B&\text { the hypothesised value is definitely false.}\\\hline C&\text { we reject the null hypothesis. }\\\hline D&\text {we don't reject the null hypothesis. }\\\hline \end{array}$

Question 37

If we do not reject the null hypothesis, we conclude that: $\begin{array}{|l|l|}\hline A&\text { there is enough statistical evidence to infer that the alternative hypothesis is true.}\\\hline B&\text {there is not enough statistical evidence to infer that the al ternative hypothesis is true. }\\\hline C&\text { there is enough statistical evidence to infer that the null hypothesis is true. }\\\hline D&\text { the test is statistically insignificant at whatever level of significance the test was conducted}\\&\text { at.}\\\hline \end{array}$

Question 38

We cannot commit a Type I error when the: $\begin{array}{|l|l|}\hline A&\text {null hypothesis is true. }\\\hline B&\text { level of significance is 0.10 .}\\\hline C&\text {null hypothesis is false. }\\\hline D&\text { test is a two-tail test. }\\\hline \end{array}$

Question 39

The power of a test is denoted by:

Question 40

The confidence interval approach can be employed to conduct tests of hypotheses. Which of the following statements is false? $\begin{array}{|l|l|}\hline A.&\text {The confidence interval approach is equivalent to the rejection region approach. }\\\hline B.&\text {The confidence interval approach has the disadvantage of complexity. }\\\hline C.&\text {One-sided confidence intervals can be used when conducting a one-tail test. }\\\hline D.&\text {The confidence interval approach does not yield a \( p \)-value. }\\\hline \end{array}$

Question 41

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

Question 42

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

Question 43

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

Question 44

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

Question 45

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

Question 46

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

Question 47

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

Question 48

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

Question 49

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

Question 50

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

Question 51

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 52

Which of the following best describes the p-value of a test? $\begin{array}{|l|l|}\hline A&\text {The \( p \)-value is the probability of getting our statistical table value of the test statistic if }\\&\text {the null hypothesized value of the population parameter, were really true. }\\\hline B&\text {The p-value is the probability of getting our cal culated test statistic or more extreme if the }\\&\text { null hypothesized value of the population parameter, were really true.}\\\hline C&\text { The p-value is the probability of getting our calculated test statistic, or more extreme, if }\\&\text {the null hypothesized value of the population parameter, were really false. }\\\hline D&\text {None of these choices are correct. }\\\hline \end{array}$

Question 53

The p-value is usually 0.05.

Question 54

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

Question 55

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

Question 56

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

Question 57

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

Question 58

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?

Question 59

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 60

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

Question 61

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

Question 62

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

Question 63

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

Question 64

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

Question 65

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 66

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

Question 67

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

Question 68

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

Question 69

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

Question 70

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 71

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

Question 72

A test for the population mean $\mu$ 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 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 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 75

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

Question 76

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

Question 77

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

Question 78

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 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 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.