Exam 13: Hypothesis Testing: Describing a Single Population

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 81

We cannot commit a Type I error when the:

(Multiple Choice)

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Question 82

In testing the hypotheses: $H _ { 0 } : \mu =$ 500 $H _ { 1 } : \mu \neq$ 500, if the value of the Z test statistic equals 2.03, then the p-value is:

(Multiple Choice)

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Question 83

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

(True/False)

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Question 84

Statisticians can translate p-values into several descriptive terms. Which of the following statements is correct?

(Multiple Choice)

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Question 85

In testing the hypotheses $H _ { 0 }$ : $\mu = 20$ . $H _ { 1 } : \mu < 20$ . the following information was given: $\sigma = 8.1 , \quad n = 100 , \quad \bar { x } = 18.1 , \quad \alpha = 0.025$ . a. Calculate the value of the test statistic. b. Set up the rejection region. c. Determine the p-value. d. Interpret the result.

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Question 86

Suppose that nine observations are drawn from a normal population whose standard deviation is 2. The observations are: 15 9 13 11 8 12 11 7 10 At 95% confidence, you want to determine whether the mean of the population from which this sample was taken is significantly different from 10. a. State the null and alternative hypotheses. b. Compute the value of the test statistic. c. Compute the p-value. d. Interpret the results.

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Question 87

In testing the hypotheses $H _ { 0 } : \mu = 50$ . $H _ { 1 } : \mu < 50$ . we found that the standardised test statistic is z = -1.59. Calculate the p-value.

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Question 88

At present, many universities in Australia are adopting the practice of having lecture recordings automatically available to students. A university lecturer is trying to investigate whether having lecture recordings available to students has significantly decreased the proportion of students passing her course. When lecture recordings were not provided to students, the proportion of students that passed her course was 80%. The lecturer takes a random sample of 25 students, when lecture recordings are offered to students, and finds that 11 students have passed the course. Is there significant evidence to support this university lecturer's claim? Use the p-value method and test at α = 0.01

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Question 89

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

(Multiple Choice)

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Question 90

In testing the hypotheses $H _ { 0 } : \mu = 60$ . $H _ { 1 } : \mu < 60$ . the following information was given: $\sigma = 5 , \quad n = 100 , \quad \bar { x } = 59 , \quad \alpha = 0.05$ . 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 91

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

(Multiple Choice)

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Question 92

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

(Multiple Choice)

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Question 93

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:

(Multiple Choice)

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Question 94

To test the hypotheses $H_ { 0 } : \mu = 40$ $H _ { 1 } : \mu \neq 40$ we draw a random sample of size 16 from a normal population whose standard deviation is 5. If we set $\alpha = 0.01$ find $\beta$ when $\mu = 37$ .

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Question 95

The confidence interval approach can be employed to conduct tests of hypotheses. Which of the following statements is false?

(Multiple Choice)

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Question 96

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. a. Calculate the p-value. b. Compute the probability of a Type II error if the true average amount of gas remaining in tanks is 3.5 litres.

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Question 97

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

(True/False)

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Question 98

A Type II error is defined as:

(Multiple Choice)

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Question 99

In a two-tail test for the population mean, the null hypothesis will be rejected at the $\alpha$ level of significance if the value of the standardised test statistic z is such that:

(Multiple Choice)

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Question 100

We cannot commit a Type I error when the:

In testing the hypotheses: $H _ { 0 } : \mu =$ 500 $H _ { 1 } : \mu \neq$ 500, if the value of the Z test statistic equals 2.03, then the p-value is:

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

Statisticians can translate p-values into several descriptive terms. Which of the following statements is correct?

In testing the hypotheses $H _ { 0 } : \mu = 50$ . $H _ { 1 } : \mu < 50$ . we found that the standardised test statistic is z = -1.59. Calculate the p-value.

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

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

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

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:

To test the hypotheses $H_ { 0 } : \mu = 40$ $H _ { 1 } : \mu \neq 40$ we draw a random sample of size 16 from a normal population whose standard deviation is 5. If we set $\alpha = 0.01$ find $\beta$ when $\mu = 37$ .

The confidence interval approach can be employed to conduct tests of hypotheses. Which of the following statements is false?

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

A Type II error is defined as:

In a two-tail test for the population mean, the null hypothesis will be rejected at the $\alpha$ level of significance if the value of the standardised test statistic z is such that:

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

Exam 13: Hypothesis Testing: Describing a Single Population

We cannot commit a Type I error when the:

In testing the hypotheses: H0:μ=H _ { 0 } : \mu =H0​:μ= 500 H1:μ≠H _ { 1 } : \mu \neqH1​:μ= 500, if the value of the Z test statistic equals 2.03, then the p-value is:

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

Statisticians can translate p-values into several descriptive terms. Which of the following statements is correct?

In testing the hypotheses H0:μ=50H _ { 0 } : \mu = 50H0​:μ=50 . H1:μ<50H _ { 1 } : \mu < 50H1​:μ<50 . we found that the standardised test statistic is z = -1.59. Calculate the p-value.

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

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

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

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:

To test the hypotheses H0:μ=40H_ { 0 } : \mu = 40H0​:μ=40 H1:μ≠40H _ { 1 } : \mu \neq 40H1​:μ=40 we draw a random sample of size 16 from a normal population whose standard deviation is 5. If we set α=0.01\alpha = 0.01α=0.01 find β\betaβ when μ=37\mu = 37μ=37 .

The confidence interval approach can be employed to conduct tests of hypotheses. Which of the following statements is false?

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

A Type II error is defined as:

In a two-tail test for the population mean, the null hypothesis will be rejected at the α\alphaα level of significance if the value of the standardised test statistic z is such that:

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: $H _ { 0 } : \mu =$ 500 $H _ { 1 } : \mu \neq$ 500, if the value of the Z test statistic equals 2.03, then the p-value is:

In testing the hypotheses $H _ { 0 } : \mu = 50$ . $H _ { 1 } : \mu < 50$ . we found that the standardised test statistic is z = -1.59. Calculate the p-value.

To test the hypotheses $H_ { 0 } : \mu = 40$ $H _ { 1 } : \mu \neq 40$ we draw a random sample of size 16 from a normal population whose standard deviation is 5. If we set $\alpha = 0.01$ find $\beta$ when $\mu = 37$ .

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

In a two-tail test for the population mean, the null hypothesis will be rejected at the $\alpha$ level of significance if the value of the standardised test statistic z is such that: