In a one-tail test for the population mean, if the null hypothesis is not rejected when the alternative hypothesis is true: $\begin{array}{|l|l|} \hline A.&\text { a Type I error is committed.}\\ \hline B.&\text {a Type II error is committed. }\\ \hline C.&\text {a correct decision is made. }\\ \hline D.&\text { a two-tail test should be used instead of a one-tail test.}\\ \hline \end{array}$

The answer of In a one-tail test for the population...

When testing whether the majority of voters in an electorate will vote for a particular candidate, which of the following sets of hypotheses are correct? $\begin{array}{|l|l|} \hline A&H_{0}: p=0.50 \\ &H_{A}: p0.50\\ &H_{\mathrm{A}}: p=0.50\\ \hline C&H_{0}: p=0.50\\ &H_{\mathrm{A}}: p>0.50\\ \hline D&\text { None of these choices are correct }\\ \hline \end{array}$

The answer of When testing whether the majority of voters...

State which of the following set of hypotheses are appropriate. Explain a. Ho: µ = 25 H1: µ ≠ 25 b. Ho: µ > 25 H1: µ = 25 c. $H _ { 0 } :$ $\bar { x } = 35$ . $H _ { 1 } : \bar { x } > 35$ . d. Ho: p = 25 H1: p ≠ 25 e. Ho: p = 0.5 H1: p > 0.5

a. Appropriate, because the population p

A Type I error occurs when we: $\begin{array}{|l|l|} \hline A.&\text { reject a false null hypothesis.}\\ \hline B.&\text { eject a true null hypothesis.}\\ \hline C.&\text {don't reject a false null hypothesis. }\\ \hline D.&\text { don't reject a true null hypothesis.}\\ \hline \end{array}$

The answer of A Type I error occurs when we:...

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: $\begin{array}{|l|l|} \hline \text { A. } & 0.0424 \\ \hline \text { B. } & 0.4788 \\ \hline \text { C. } & 0.9576 . \\ \hline \text { D. } & 0.0212 \\ \hline \end{array}$

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

Exam 13: Hypothesis Testing: Describing a Single Population

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

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Question 81

In testing the hypotheses: H₀: $\mu$ = 950 H₁: $\mu$ $\neq$ $\neq$ 950, the following information was given: ? = 1000, $\alpha$ = 0.05, $\mu$ = 180 and n = 75. Determine $\mu$ .

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Question 82

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?

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Question 83

When testing whether the majority of voters in an electorate will vote for a particular candidate, which of the following sets of hypotheses are correct? A :p=0.50 :p<0.50 B :p>0.50 :p=0.50 C :p=0.50 :p>0.50 D None of these choices are correct

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Question 84

State which of the following set of hypotheses are appropriate. Explain a. Ho: µ = 25 H₁: µ ≠ 25 b. Ho: µ > 25 H₁: µ = 25 c. $H _ { 0 } :$ $\bar { x } = 35$ . $H _ { 1 } : \bar { x } > 35$ . d. Ho: p = 25 H₁: p ≠ 25 e. Ho: p = 0.5 H₁: p > 0.5

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Question 85

In a two-tail test for the population mean, if the null hypothesis is rejected when the alternative hypothesis is true, a Type I error is committed.

(True/False)

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Question 86

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.

(True/False)

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Question 87

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 88

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.

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Question 89

In testing the hypotheses: H₀: $\mu$ = 950 H₁: $\mu$ $\neq$ $\neq$ 950, the following information was given: ? = 1000, $\alpha$ = 0.05, $\mu$ = 180 and n = 75. It was found that $\beta$ = 0.2061. a. Recalculate $\beta$ if n = 100. b. What is the effect of increasing the sample size on the value of $\beta$ ?

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Question 90

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? 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.

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Question 91

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.

(True/False)

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Question 92

A random sample of 100 observations from a normal population whose standard deviation is 50 produced a mean of 75. Does this statistic provide sufficient evidence at the 5% level of significance to infer that the population mean is not 80?

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Question 93

In testing the hypotheses: $H _ { 0 } : \mu = 25$ $H _ { 1 } : \mu \neq 25$ , 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.

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Question 94

When using a t-test to test the population mean, the degrees of freedom are n - 1.

(True/False)

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Question 95

When testing a value of the population proportion, we must do a Z-test.

(True/False)

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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 occurs when we: A. reject a false null hypothesis. B. eject a true null hypothesis. C. don't reject a false null hypothesis. D. don't reject a true null hypothesis.

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Question 98

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: A. 0.0424 B. 0.4788 C. 0.9576. D. 0.0212

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Question 99

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

(True/False)

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Question 100

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

In testing the hypotheses: H₀: $\mu$ = 950 H₁: $\mu$ $\neq$ $\neq$ 950, the following information was given: ? = 1000, $\alpha$ = 0.05, $\mu$ = 180 and n = 75. Determine $\mu$ .

When testing whether the majority of voters in an electorate will vote for a particular candidate, which of the following sets of hypotheses are correct? A :p=0.50 :p<0.50 B :p>0.50 :p=0.50 C :p=0.50 :p>0.50 D None of these choices are correct

State which of the following set of hypotheses are appropriate. Explain a. Ho: µ = 25 H₁: µ ≠ 25 b. Ho: µ > 25 H₁: µ = 25 c. $H _ { 0 } :$ $\bar { x } = 35$ . $H _ { 1 } : \bar { x } > 35$ . d. Ho: p = 25 H₁: p ≠ 25 e. Ho: p = 0.5 H₁: p > 0.5

In a two-tail test for the population mean, if the null hypothesis is rejected when the alternative hypothesis is true, a Type I error is committed.

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.

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 random sample of 100 observations from a normal population whose standard deviation is 50 produced a mean of 75. Does this statistic provide sufficient evidence at the 5% level of significance to infer that the population mean is not 80?

In testing the hypotheses: $H _ { 0 } : \mu = 25$ $H _ { 1 } : \mu \neq 25$ , 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.

When using a t-test to test the population mean, the degrees of freedom are n - 1.

When testing a value of the population proportion, we must do a Z-test.

A Type I error occurs when we: A. reject a false null hypothesis. B. eject a true null hypothesis. C. don't reject a false null hypothesis. D. don't reject a true null hypothesis.

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: A. 0.0424 B. 0.4788 C. 0.9576. D. 0.0212

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

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

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

In testing the hypotheses: H0 : μ\muμ = 950 H1 : μ\muμ≠\neq=≠\neq= 950, the following information was given: ? = 1000, α\alphaα = 0.05, μ\muμ = 180 and n = 75. Determine μ\muμ .

When testing whether the majority of voters in an electorate will vote for a particular candidate, which of the following sets of hypotheses are correct? A :p=0.50 :p<0.50 B :p>0.50 :p=0.50 C :p=0.50 :p>0.50 D None of these choices are correct

State which of the following set of hypotheses are appropriate. Explain a. Ho: µ = 25 H1: µ ≠ 25 b. Ho: µ > 25 H1: µ = 25 c. H0:H _ { 0 } :H0​: xˉ=35\bar { x } = 35xˉ=35 . H1:xˉ>35H _ { 1 } : \bar { x } > 35H1​:xˉ>35 . d. Ho: p = 25 H1: p ≠ 25 e. Ho: p = 0.5 H1: p > 0.5

In a two-tail test for the population mean, if the null hypothesis is rejected when the alternative hypothesis is true, a Type I error is committed.

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.

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 random sample of 100 observations from a normal population whose standard deviation is 50 produced a mean of 75. Does this statistic provide sufficient evidence at the 5% level of significance to infer that the population mean is not 80?

When using a t-test to test the population mean, the degrees of freedom are n - 1.

When testing a value of the population proportion, we must do a Z-test.

A Type I error occurs when we: A. reject a false null hypothesis. B. eject a true null hypothesis. C. don't reject a false null hypothesis. D. don't reject a true null hypothesis.

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: A. 0.0424 B. 0.4788 C. 0.9576. D. 0.0212

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

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: $\mu$ = 950 H₁: $\mu$ $\neq$ $\neq$ 950, the following information was given: ? = 1000, $\alpha$ = 0.05, $\mu$ = 180 and n = 75. Determine $\mu$ .

State which of the following set of hypotheses are appropriate. Explain a. Ho: µ = 25 H₁: µ ≠ 25 b. Ho: µ > 25 H₁: µ = 25 c. $H _ { 0 } :$ $\bar { x } = 35$ . $H _ { 1 } : \bar { x } > 35$ . d. Ho: p = 25 H₁: p ≠ 25 e. Ho: p = 0.5 H₁: p > 0.5

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: A. 0.0424 B. 0.4788 C. 0.9576. D. 0.0212