The critical values z $\mathrm{\alpha}$ or z $\alpha / 2$ are the boundary values for the: $\begin{array}{|l|l|} \hline A.&\text { rejection region(s). } \\ \hline B.&\text { level of significance. } \\ \hline C. &\text { power of the test. } \\ \hline D.& \text { Type II error. } \\ \hline \end{array}$

The answer of The critical values z $\mathrm{\alpha}$ or z...

If we reject the null hypothesis, we conclude that: $\begin{array}{|l|l|} \hline \text { A. } & \text { there is enough statistical evidence to infer that the alternative hypothesis is true. } \\ \hline \text { B. } & \text { there is not enough statistical evidence to infer that the al ternative hypothesis is true. } \\ \hline \text { C. } & \text { there is enough statistical evidence to infer that the null hypothesis is true. } \\ \hline \text { D. } & \text { the test is statistically insignificant at whatever level of significance the test was conducted } \\ &\text { at. }\\\hline \end{array}$

The answer of If we reject the null hypothesis, we...

For a given level of significance, if the sample size decreases, the probability of a Type II error will: $\begin{array}{|l|l|} \hline A&\text {remain the same. }\\ \hline B&\text {increase. }\\ \hline C&\text { decrease.}\\ \hline D&\text {be equal to 1.0 regardless of the value of \( \alpha $. }\\ \hline \end{array}\)

The answer of For a given level of significance, if...

In a criminal trial, a Type II error is made when: $\begin{array}{|l|l|} \hline A&\text {a guilty defendant is acquitted. }\\ \hline B&\text { an innocent person is convicted.}\\ \hline C&\text {a guilty defendant is convicted. }\\ \hline D&\text {an innocent person is acquitted. }\\ \hline \end{array}$

The answer of In a criminal trial, a Type II...

The manager of a fast food restaurant is investigating the average number of fries per Large-sized offered to customers, to assess quality control. The manager took a random sample of five Large-sized orders of fries, and counted the number of fries per serve, with the results given below: $\begin{array}{|r|r|r|r|r|} \hline73 & 75 & 83 & 68 & 78 \\ \hline \end{array}$ Assume that the number of French fries served at this fast food restaurant is normally distributed. Can we infer at the 5% significance level that the average number of fries served in a Large-sized order of fries at this fast food restaurant is over 70?

H 0 : μ = 70. H 1 : μ > 70. Rejection region:

Exam 13: Hypothesis Testing: Describing a Single Population

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 and that $\beta$ = 0.2061. a. Recalculate $\beta$ if $\alpha$ is lowered from 0.05 to 0.01. b. What is the effect of decreasing the significance level on the value of $\beta$ ?

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Question 41

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

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Question 42

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.

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Question 43

The critical values z $\mathrm{\alpha}$ or z $\alpha / 2$ are the boundary values for the: A. rejection region(s). B. level of significance. C. power of the test. D. Type II error.

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Question 44

Consider the hypotheses $H _ { 0 } : \mu = 950$ $H _ { 1 } : \mu \neq 950$ . Assume that $\mu = 1000 ,$ $\alpha = 0.10$ $\sigma = 200$ , and n = 25 and $\beta$ = 0.6535 Recalculate $\beta$ if $\alpha$ is lowered from 0.10 to 0.05.

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Question 45

In any given test, it is possible to commit the Type I and Type II errors at the same time.

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Question 46

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 47

Given that s = 15, n = 50, x-bar = 17.5, $\alpha$ = 0.05, test the following hypotheses: H₀ : $\mu$ = 22. H₁ : $\mu$ $\neq$ 22

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Question 48

A two-tail test for the population mean $\mu$ produces a test-statistic z = -1.43. The p-value associated with the test is 0.0764.

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Question 49

There is an inverse relationship between the probabilities of Type I and Type II errors.

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Question 50

If we reject the null hypothesis, we conclude that: 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 al ternative 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.

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Question 51

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

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Question 52

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

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Question 53

Suppose that we reject a null hypothesis at the 0.05 level of significance. For which of the following $\alpha$ -values do we also reject the null hypothesis? A. 0.06 B. 0.04 C. 0.03 D. 0.02

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Question 54

For a given level of significance, if the sample size decreases, the probability of a Type II error will: A remain the same. B increase. C decrease. D be equal to 1.0 regardless of the value of \alpha .

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Question 55

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. Can we conclude at the 5% significance level that the true mean number of months families in this city have been living in their current homes is at least 30 months?

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Question 56

Consider the hypotheses $H _ { 0 } : \mu = 950$ $H _ { 1 } : \mu \neq 950$ . Assume that $\mu = 1000 ,$ $\alpha = 0.10$ $\sigma = 200$ , and n = 25 and $\beta$ = 0.6535 Calculate the power of the test.

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Question 57

In a criminal trial, a Type II error is made when: A a guilty defendant is acquitted. B an innocent person is convicted. C a guilty defendant is convicted. D an innocent person is acquitted.

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Question 58

The manager of a fast food restaurant is investigating the average number of fries per Large-sized offered to customers, to assess quality control. The manager took a random sample of five Large-sized orders of fries, and counted the number of fries per serve, with the results given below: 73 75 83 68 78 Assume that the number of French fries served at this fast food restaurant is normally distributed. Can we infer at the 5% significance level that the average number of fries served in a Large-sized order of fries at this fast food restaurant is over 70?

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Question 59

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

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Question 60

Exam 13: Hypothesis Testing: Describing a Single Population

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

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.

The critical values z α\mathrm{\alpha}α or z α/2\alpha / 2α/2 are the boundary values for the: A. rejection region(s). B. level of significance. C. power of the test. D. Type II error.

In any given test, it is possible to commit the Type I and Type II errors at the same time.

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 = 0.01 ,α=0.01, find β\betaβ when μ=37\mu = 37μ=37 .

Given that s = 15, n = 50, x-bar = 17.5, α\alphaα = 0.05, test the following hypotheses: H0 : μ\muμ = 22. H1 : μ\muμ ≠\neq= 22

A two-tail test for the population mean μ\muμ produces a test-statistic z = -1.43. The p-value associated with the test is 0.0764.

There is an inverse relationship between the probabilities of Type I and Type II errors.

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

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

Suppose that we reject a null hypothesis at the 0.05 level of significance. For which of the following α\alphaα -values do we also reject the null hypothesis? A. 0.06 B. 0.04 C. 0.03 D. 0.02

For a given level of significance, if the sample size decreases, the probability of a Type II error will: A remain the same. B increase. C decrease. D be equal to 1.0 regardless of the value of \alpha .

Consider the hypotheses H0:μ=950H _ { 0 } : \mu = 950H0​:μ=950 H1:μ≠950H _ { 1 } : \mu \neq 950H1​:μ=950 . Assume that μ=1000,\mu = 1000 ,μ=1000, α=0.10\alpha = 0.10α=0.10 σ=200\sigma = 200σ=200 , and n = 25 and β\betaβ = 0.6535 Calculate the power of the test.

In a criminal trial, a Type II error is made when: A a guilty defendant is acquitted. B an innocent person is convicted. C a guilty defendant is convicted. D an innocent person is acquitted.

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

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

The critical values z $\mathrm{\alpha}$ or z $\alpha / 2$ are the boundary values for the: A. rejection region(s). B. level of significance. C. power of the test. D. Type II error.

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 $\mu = 37$ .

Given that s = 15, n = 50, x-bar = 17.5, $\alpha$ = 0.05, test the following hypotheses: H₀ : $\mu$ = 22. H₁ : $\mu$ $\neq$ 22

A two-tail test for the population mean $\mu$ produces a test-statistic z = -1.43. The p-value associated with the test is 0.0764.

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

Suppose that we reject a null hypothesis at the 0.05 level of significance. For which of the following $\alpha$ -values do we also reject the null hypothesis? A. 0.06 B. 0.04 C. 0.03 D. 0.02

Consider the hypotheses $H _ { 0 } : \mu = 950$ $H _ { 1 } : \mu \neq 950$ . Assume that $\mu = 1000 ,$ $\alpha = 0.10$ $\sigma = 200$ , and n = 25 and $\beta$ = 0.6535 Calculate the power of the test.