Question 1

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

Accepted Answer

A) True 
 B)False

Question 2

The probability of a Type II error is denoted by:

Accepted Answer

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

Question 3

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?

Accepted Answer

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. 
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 4

A Type I error occurs when we:

Accepted Answer

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. 
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 5

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.

Accepted Answer

A) True 
 B)False

Question 6

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.

Accepted Answer

A) True 
 B)False

Question 7

In testing the hypotheses: $H_ { 0 } : \mu = 40$ $H _ { 1 } : \mu \neq 40$ the following information was given: $\sigma = 5.5 , \quad n = 25 , \quad \bar { x } = 42 , \quad \alpha = 0.10$ , and the sampled population is normally distributed.
a. Calculate the value of the test statistic.
b. Set up the rejection region.
c. Determine the p-value.
d. Interpret the result.

Accepted Answer

a. z = 1.818.
b. |z|

Question 8

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

Accepted Answer

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

Question 9

For each of the following statements, state the population parameter of interest, state the appropriate null and alternative hypotheses and indicate whether the appropriate test will be a two-tailed, a left tailed or a right tailed test.
a. The average age a person registers to vote in Australia is greater than 20 years.
b. A minority of office workers purchase their morning coffee.
c. The average number of hours spent on a computer per day.
d. The majority of students in a particular university course who attend lectures has changed from 75%, since lecture recordings have become freely available to students.

Accepted Answer

a. The population parameter of interest

Question 10

With the following p-values, would you reject or fail to reject the null hypothesis? What would you say about the test?
a. p-value = 0.0025.
b. p-value = 0.0328.
c. p-value = 0.0795.
d. p-value = 0.1940.

Accepted Answer

a. There is overwhelming evidence to rej

Question 11

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:

Accepted Answer

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. 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 12

A random sample of 100 families in a large city revealed that on the average these families have been living in their current homes for 35 months. From previous analyses, we know that the population standard deviation is 30 months.
Compute the probability of a Type II error if the true mean number of months families in this city have been living in their current homes is 29.

Accepted Answer

A Type II error has

Question 13

If we reject the null hypothesis, we conclude that:

Accepted Answer

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. 
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 14

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

Accepted Answer

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. 
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 15

The rejection region for testing the hypotheses $H _ { 0 } : \mu =$ 80. $H _ { 1 } : \mu$ < 80. at the 0.10 level of significance is:

Accepted Answer

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

Question 16

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

Accepted Answer

A) True 
 B)False

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

A) True 
 B)False

Question 20

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

Accepted Answer

A) True 
 B)False

Exam 13: Hypothesis Testing: Describing a Single Population

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

The probability of a Type II error is denoted by:

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

A Type I error occurs when we:

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.

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.

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

With the following p-values, would you reject or fail to reject the null hypothesis? What would you say about the test? a. p-value = 0.0025. b. p-value = 0.0328. c. p-value = 0.0795. d. p-value = 0.1940.

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:

If we reject the null hypothesis, we conclude that:

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

The rejection region for testing the hypotheses H0:μ=H _ { 0 } : \mu =H0​:μ= 80. H1:μH _ { 1 } : \muH1​:μ < 80. at the 0.10 level of significance is:

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

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

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

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

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

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

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?

The rejection region for testing the hypotheses $H _ { 0 } : \mu =$ 80. $H _ { 1 } : \mu$ < 80. at the 0.10 level of significance is:

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

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