Question 1

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 2

In testing the hypotheses:
H0: μ = 25
HA: μ F1F1F1S1F1F1F10 25
a random sample of 36 observations drawn from a normal population, produced a mean of 22.8 and a standard deviation of 10
What is the conclusion for this hypothesis test, at 5% significance level.

Accepted Answer

Test statistic: t = -1.32.
Rejection reg

Question 3

Consider the hypotheses
H0: μ = 950
HA: μ F1F1F1S1F1F1F10 950
Assume that μ = 1000, F1F1F1S1F1F1F10 = 200, n = 25, F1F1F1S1F1F1F10 = 0.10 and F1F1F1S1F1F1F10 = 0.6535. Calculate the power of the test.

Accepted Answer

Power = 1

Question 4

In testing the hypotheses
H0: μ = 20
HA: μ < 20F1F1F1S1F1F1F10
the following information was given: F1F1F1S1F1F1F10 = 8.1, n = 100, $\bar { X }$ = 18.1, α = 0.025.
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 = -2.346.
b. Z < -z0.025

Question 5

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

Accepted Answer

A) True 
 B)False

Question 6

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

Accepted Answer

A) True 
 B)False

Question 7

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 8

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

Accepted Answer

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. 
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 9

Consider the hypotheses
H0: μ = 950
HA: μ F1F1F1S1F1F1F10 950
Assume that μ = 1000, F1F1F1S1F1F1F10 = 200, n = 25, F1F1F1S1F1F1F10 = 0.10. Calculate F1F1F1S1F1F1F10, the probability of a Type II error.

Accepted Answer

F1F1F1S1F1F1F10 = P

Question 10

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 11

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.

Accepted Answer

A) True 
 B)False

Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

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.

Accepted Answer

A) True 
 B)False

Question 14

The critical values zα or zα/2 are the boundary values for the:

Accepted Answer

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

Question 15

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

Accepted Answer

A) True 
 B)False

Question 16

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: F1F1F1S1F1F1F10 = 6, HA: F1F1F1S1F1F1F10 < 6 should be used.

Accepted Answer

A) True 
 B)False

Question 17

During the Gulf War, a government official claimed that the average car owner refilled the fuel tank when there was more than 3 litres of petrol left. To check the claim, 10 cars were surveyed as they entered a service station. The amount of petrol (in litres) was measured and recorded as shown below. $\begin{array}{|r|r|r|r|r|r|r|r|r|r|}
\hline3&5&3&2&3&3&2&6&4&1\
\hline
\end{array}$ Assume that the amount of petrol remaining in the tanks is normally distributed with a standard deviation of 1 litre.
Can we conclude at the 10% significance level that the official was correct?

Accepted Answer

H0: μ = 3
HA: μ > 3
Test stati

Question 18

A Type II error is defined as:

Accepted Answer

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. 
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 19

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:

Accepted Answer

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. 
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 20

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:

Accepted Answer

A) H0: F1F1F1S1F1F1F10 = 1200 HA: F1F1F1S1F1F1F10 1200 HA: F1F1F1S1F1F1F10 =1200. C) H0: F1F1F1S1F1F1F10 = 1200 HA: F1F1F1S1F1F1F10 > 1200. D) H0: F1F1F1S1F1F1F10 < 1200 HA: F1F1F1S1F1F1F10 = 1200. A) H0: F1F1F1S1F1F1F10 = 1200 HA: F1F1F1S1F1F1F10 1200 HA: F1F1F1S1F1F1F10 =1200. C) H0: F1F1F1S1F1F1F10 = 1200 HA: F1F1F1S1F1F1F10 > 1200. D) H0: F1F1F1S1F1F1F10 < 1200 HA: F1F1F1S1F1F1F10 = 1200.

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

In testing the hypotheses: H0: μ = 25 HA: μ  25 a random sample of 36 observations drawn from a normal population, produced a mean of 22.8 and a standard deviation of 10 What is the conclusion for this hypothesis test, at 5% significance level.

Consider the hypotheses H0: μ = 950 HA: μ  950 Assume that μ = 1000,  = 200, n = 25,  = 0.10 and  = 0.6535. Calculate the power of the test.

In testing the hypotheses H0: μ = 20 HA: μ < 20 the following information was given:  = 8.1, n = 100, $\bar { X }$ = 18.1, α = 0.025. a. Calculate the value of the test statistic. b. Set up the rejection region. c. Determine the p-value. d. Interpret the result.

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

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

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

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

Consider the hypotheses H0: μ = 950 HA: μ  950 Assume that μ = 1000,  = 200, n = 25,  = 0.10. Calculate , the probability of a Type II error.

The probability of a Type II error is denoted by:

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.

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

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.

The critical values zα or zα/2 are the boundary values for the:

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

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.

A Type II error is defined as:

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 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:

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

Exam 12: Hypothesis Testing: Describing a Single Population

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

In testing the hypotheses: H0: μ = 25 HA: μ  25 a random sample of 36 observations drawn from a normal population, produced a mean of 22.8 and a standard deviation of 10 What is the conclusion for this hypothesis test, at 5% significance level.

Consider the hypotheses H0: μ = 950 HA: μ  950 Assume that μ = 1000,  = 200, n = 25,  = 0.10 and  = 0.6535. Calculate the power of the test.

In testing the hypotheses H0: μ = 20 HA: μ < 20 the following information was given:  = 8.1, n = 100, Xˉ\bar { X }Xˉ = 18.1, α = 0.025. a. Calculate the value of the test statistic. b. Set up the rejection region. c. Determine the p-value. d. Interpret the result.

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

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

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

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

Consider the hypotheses H0: μ = 950 HA: μ  950 Assume that μ = 1000,  = 200, n = 25,  = 0.10. Calculate , the probability of a Type II error.

The probability of a Type II error is denoted by:

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.

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

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.

The critical values zα or zα/2 are the boundary values for the:

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

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.

A Type II error is defined as:

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 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:

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

In testing the hypotheses H0: μ = 20 HA: μ < 20 the following information was given:  = 8.1, n = 100, $\bar { X }$ = 18.1, α = 0.025. a. Calculate the value of the test statistic. b. Set up the rejection region. c. Determine the p-value. d. Interpret the result.

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.