Question 1

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

Accepted Answer

A) True 
 B)False

Question 2

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 3

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

Accepted Answer

A) True 
 B)False

Question 4

A drug company is interested in the effectiveness of a new sleeping pill. A random sample of 50 people try the new sleeping pill and the number of additional hours of sleep (compared with the nights without any sleeping pill), X, are recorded. The sample standard deviation of X is 3 hours.
a. State the null and alternative hypotheses for the claim that the new drug increases the number of hours of sleep at least by 2 hours on average.
b. Using a standardised test statistic, test the hypothesis at the 5% level of significance if the sample mean of additional hours of sleep is 2.2 hours.

Accepted Answer

a. H0: μ = 2.
HA: μ > 2F1F1F1S1F1F1F10.

Question 5

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 and the power of the test is 0.3465. Interpret the meaning of the power in the previous question.

Accepted Answer

The probability of rejecting t

Question 6

The manager of a sports store is considering trading on Public holidays. She believes that a majority of consumers would consider visiting the sports store on a Public holiday.
She takes a random sample of 50 customers and finds that 29 would visit the sports store on a Public holiday. Is there significant evidence to support the manager's claim? Test at the 5% level of significance.

Accepted Answer

Given that the sample is random, the sam

Question 7

In testing the hypotheses
H0: F1F1F1S1F1F1F10 = 50
HA: F1F1F1S1F1F1F10 < 50
we found that the standardised test statistic is Z = -1.59. Calculate the p-value.

Accepted Answer

The answer of In testing the hypotheses
H0: F1F1F1S1F1F1F10 = 50
HA:...

Question 8

In our justice system, judges instruct juries to find the defendant guilty only if there is evidence 'beyond a reasonable doubt'. In general, what would be the result if judges instructed juries:
a. to compromise between Type I and Type II errors?
b. never to commit a Type I error?
c. never to commit a Type II error?

Accepted Answer

a. An innocent person might be wrongly c

Question 9

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

Accepted Answer

A) a guilty defendant is acquitted. 
B) an innocent person is convicted. 
C) a guilty defendant is convicted. 
D) an innocent person is acquitted. 
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 10

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 11

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

Accepted Answer

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. 
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 12

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

Accepted Answer

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. 
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 13

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

Accepted Answer

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

Accepted Answer

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. 
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 15

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 16

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

Accepted Answer

A) True 
 B)False

Question 17

In testing the hypotheses:
H0: μ = 25
HA: μ F1F1F1S1F1F1F10 25
a random sample of 36 observations drawn from a normal population whose standard deviation is 10 produced a mean of 22.8.
Explain briefly how to use the confidence interval in the previous question to test the hypothesis.

Accepted Answer

Since the hypothesised value μ

Question 18

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

Accepted Answer

A) True 
 B)False

Question 19

A Type I error occurs when we:

Accepted Answer

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. 
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 20

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:

Accepted Answer

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. 
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.

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

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

Consider the hypotheses H0: μ = 950 HA: μ  950 Assume that μ = 1000,  = 200, n = 25,  = 0.10 and  = 0.6535 and the power of the test is 0.3465. Interpret the meaning of the power in the previous question.

In testing the hypotheses H0:  = 50 HA:  < 50 we found that the standardised test statistic is Z = -1.59. Calculate the p-value.

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

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.

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

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

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

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

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

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

In testing the hypotheses: H0: μ = 25 HA: μ  25 a random sample of 36 observations drawn from a normal population whose standard deviation is 10 produced a mean of 22.8. Explain briefly how to use the confidence interval in the previous question to test the hypothesis.

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

A Type I error occurs when we:

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:

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

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

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

Consider the hypotheses H0: μ = 950 HA: μ  950 Assume that μ = 1000,  = 200, n = 25,  = 0.10 and  = 0.6535 and the power of the test is 0.3465. Interpret the meaning of the power in the previous question.

In testing the hypotheses H0:  = 50 HA:  < 50 we found that the standardised test statistic is Z = -1.59. Calculate the p-value.

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

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.

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

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

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

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

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

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

In testing the hypotheses: H0: μ = 25 HA: μ  25 a random sample of 36 observations drawn from a normal population whose standard deviation is 10 produced a mean of 22.8. Explain briefly how to use the confidence interval in the previous question to test the hypothesis.

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

A Type I error occurs when we:

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:

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

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