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

The answer of If the value of the sample mean...

The p-value criterion for hypothesis testing is to retain the null hypothesis if: $\begin{array}{|l|l|} \hline A&p \text {-value }=\alpha \\ \hline B&p \text {-value }\alpha\\ \hline D&-\alpha \text {p-value }<\alpha\\ \hline \end{array}$

The answer of The p-value criterion for hypothesis testing is...

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: $\begin{array}{|l|l|} \hline\text { A. } & 0.064 . \\ \hline \text { B. } & 0.080 \\ \hline \text { C. } & 0.016 . \\ \hline \text { D. } & 0.066 . \\ \hline \end{array}$

The answer of In a one-tail test, the p-value is...

In testing the hypotheses $H _ { 0 } : \mu =$ 75. $H _ { 1 } :$ $\mu$ < 75. if the value of the Z test statistic equals 1.78, then the p-value is: $\begin{array}{|l|l|} \hline \text { A. } & 0.0 .375 \\ \hline \text { B. } & 0.4625 \\ \hline \text { C. } & 0.9625 \\ \hline \text { D. } & 0.5375 \\ \hline \end{array}$

The answer of In testing the hypotheses \(H _ {...

The power of a test is denoted by: $\begin{array}{|l|l|} \hline \text { A. } & \alpha . \\ \hline \text { B. } & \beta \\ \hline \text { C. } & 1-\alpha \\ \hline \text { D. } & 1-\beta \\ \hline \end{array}$

The answer of The power of a test is denoted...

The probability of a Type I error is denoted by: $\begin{array}{|l|l|} \hline \text { A. } & \beta . \\ \hline \text { B. } & 1-\beta \\ \hline \text { C. } & \alpha . \\ \hline \text { D. } & 1-\alpha . \\ \hline \end{array}$

The answer of The probability of a Type I error...

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

The answer of We cannot commit a Type I error...

Exam 13: Hypothesis Testing: Describing a Single Population

A Type II error is defined as: A. rejecting a true null hypothesis. B. rejecting a fal se null hypothesis. C. not rejecting a true null hypothesis. D. not rejecting a false null hypothesis.

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Question 1

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D

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

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Question 2

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True

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. 3 5 3 2 3 3 2 6 4 1 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?

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Question 3

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$H _ { 0 } : \mu = 3$ . $H _ { 1 } : \mu > 3$ .
Test statistic: z = 0.63.
Rejection region: z > $z _ { .10 }$ = 1.28.
Conclusion: Don't reject ${ H } _ { 0 }$ . Conclude that the official was incorrect.

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

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Question 4

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

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Question 5

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

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Question 6

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. :\mu50 :\mu<50 B. :\mu=50 :\mu50 C. :\mu50 :\mu=50 D. :\mu=50 :\mu>50

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Question 7

In testing the hypotheses $H _ { 0 } : \mu = 24.4$ . $H _ { 1 } : \mu > 24.4$ . the following information was given: $\sigma = 7.6 , \quad n = 60 , \quad \bar { x } = 25.52 , \quad \alpha = 0.06$ . a. Calculate the value of the test statistic. b. Set up the rejection region. c. Determine the p-value. d. Interpret the result.

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Question 8

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

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Question 9

The p-value criterion for hypothesis testing is to retain the null hypothesis if: A p -value =\alpha B p -value <\alpha C p -value >\alpha D -\alpha p-value <\alpha

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Question 10

If we do not reject the null hypothesis, we conclude that there is enough statistical evidence to infer that the null hypothesis is true.

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Question 11

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

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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.

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Question 13

In testing the hypotheses $H _ { 0 } : \mu =$ 75. $H _ { 1 } :$ $\mu$ < 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

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Question 14

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.

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Question 15

The power of a test is denoted by: A. \alpha. B. \beta C. 1-\alpha D. 1-\beta

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Question 16

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

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Question 17

The probability of a Type I error is denoted by: A. \beta. B. 1-\beta C. \alpha. D. 1-\alpha.

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Question 18

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.

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Question 19

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

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Question 20

Exam 13: Hypothesis Testing: Describing a Single Population

A Type II error is defined as: A. rejecting a true null hypothesis. B. rejecting a fal se null hypothesis. C. not rejecting a true null hypothesis. D. not rejecting a false null hypothesis.

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

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.

If the value of the sample mean xˉ\bar { x }xˉ is close enough to the hypothesised value of the population mean μ\muμ , then: A the hypothesised value is definitely true. B the hypothesised value is definitely false. C we reject the null hypothesis. D we don't reject the null hypothesis.

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. :\mu50 :\mu<50 B. :\mu=50 :\mu50 C. :\mu50 :\mu=50 D. :\mu=50 :\mu>50

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

The p-value criterion for hypothesis testing is to retain the null hypothesis if: A p -value =\alpha B p -value <\alpha C p -value >\alpha D -\alpha p-value <\alpha

If we do not reject the null hypothesis, we conclude that there is enough statistical evidence to infer that the null hypothesis is true.

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

In testing the hypotheses H0:μ=H _ { 0 } : \mu =H0​:μ= 75. H1:H _ { 1 } :H1​: μ\muμ < 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

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.

The power of a test is denoted by: A. \alpha. B. \beta C. 1-\alpha D. 1-\beta

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

The probability of a Type I error is denoted by: A. \beta. B. 1-\beta C. \alpha. D. 1-\alpha.

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.

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

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

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

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

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

In testing the hypotheses $H _ { 0 } : \mu =$ 75. $H _ { 1 } :$ $\mu$ < 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