Exam 11: Introduction to Hypothesis Testing

Watching the News A researcher claims viewers spend an average of 40 minutes per day watching the news.You think the average is higher than that.In testing your hypotheses H₀: $\mu$ = 40 vs.H₁: $\mu$ > 40,the following information came from your random sample of viewers: $\bar { X }$ = 42 minutes,n = 25.Assume $\sigma$ = 5.5,and $\alpha$ = 0.10. -{Watching the News Narrative} Determine the p-value.

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Question 1

Correct Answer:

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0.0344

Which of the following p-values will lead us to reject the null hypothesis if the level of significance equals 0.05?

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Question 2

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Production Filling A production filling operation has a historical standard deviation of 6 ounces.When in proper adjustment,the mean filling weight for the production process is 50 ounces.A quality control inspector periodically selects at random 36 containers and uses the sample mean filling weight to see if the process is in proper adjustment. -{Production Filling Narrative} State the null and alternative hypotheses.

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Question 3

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H₀: $\mu$ = 50 vs.H₁: $\mu$ $\neq$ 50

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

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Question 4

Increasing the probability of a Type I error will increase the probability of a Type II error.

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Question 5

Marathon Runners A researcher wants to study the average miles run per day for marathon runners.In testing the hypotheses: H₀: $\mu$ = 25 miles vs.H₁: $\mu$ $\neq$ 25 miles,a random sample of 36 marathon runners drawn from a normal population whose standard deviation is 10,produced a mean of 22.8 miles weekly. -{Marathon Runners Narrative} Compute the value of the test statistic and specify the rejection region associated with 5% significance level.

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Question 6

Rechargeable Batteries A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours).In testing the hypotheses,H₀: $\mu$ = 950 hours vs.H₁: $\mu$ $\neq$ 950 hours,a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours. -{Rechargeable Batteries Narrative} Review the results of the previous questions.What is the effect of increasing the sample size on the value of $\beta$ ?

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Question 7

A spouse suspects that the average amount of money spent on Christmas gifts for immediate family members is above $1,200.The correct set of hypotheses is:

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Question 8

The p-value is the probability that the null hypothesis is true.

(True/False)

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Question 9

For a given level of significance,if the sample size is increased,the probability of committing a Type II error will decrease.

(True/False)

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Question 10

A sample is used to obtain a 95% confidence interval for the mean of a population.The confidence interval goes from 10.89 to 13.21.If the same sample had been used to test H₀: $\mu$ = 12 vs.H₁: $\mu$ $\neq$ 12,H₀ could not be rejected at the 0.05 level.

(True/False)

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Question 11

By ____________________ the significance level,you increase the probability of a Type II error.

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Question 12

The power of a test plus the probability of a Type II error equals ____________________.

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Question 13

A two-tail test for the population mean $\mu$ produces a test-statistic z = 1.89.The p-value associated with the test is 0.0588.

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Question 14

If we want to compute the probability of a Type II error,which of the following statements is false?

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Question 15

Reducing the probability of a Type I error also reduces the probability of a Type II error.

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Question 16

The power of a test is denoted by:

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Question 17

In a criminal trial,a Type I error is made when an innocent person is convicted.

(True/False)

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Question 18

In testing the hypotheses H₀: $\mu$ = 50 vs.H₁: $\mu$ < 50,we found that the standardized test statistic is z = -1.59.Calculate the p-value,and state your conclusion if $\alpha$ = .025.

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Question 19

Explain why a Type I error and a Type II error have an inverse relationship.

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Question 20

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Exam 11: Introduction to Hypothesis Testing

Which of the following p-values will lead us to reject the null hypothesis if the level of significance equals 0.05?

If a sample size is increased at a given α\alphaα level,the probability of committing a Type II error is increased.

Increasing the probability of a Type I error will increase the probability of a Type II error.

A spouse suspects that the average amount of money spent on Christmas gifts for immediate family members is above $1,200.The correct set of hypotheses is:

The p-value is the probability that the null hypothesis is true.

For a given level of significance,if the sample size is increased,the probability of committing a Type II error will decrease.

A sample is used to obtain a 95% confidence interval for the mean of a population.The confidence interval goes from 10.89 to 13.21.If the same sample had been used to test H0: μ\muμ = 12 vs.H1: μ\muμ≠\neq= 12,H0 could not be rejected at the 0.05 level.

By ____________________ the significance level,you increase the probability of a Type II error.

The power of a test plus the probability of a Type II error equals ____________________.

A two-tail test for the population mean μ\muμ produces a test-statistic z = 1.89.The p-value associated with the test is 0.0588.

If we want to compute the probability of a Type II error,which of the following statements is false?

Reducing the probability of a Type I error also reduces the probability of a Type II error.

The power of a test is denoted by:

In a criminal trial,a Type I error is made when an innocent person is convicted.

In testing the hypotheses H0: μ\muμ = 50 vs.H1: μ\muμ < 50,we found that the standardized test statistic is z = -1.59.Calculate the p-value,and state your conclusion if α\alphaα = .025.

Explain why a Type I error and a Type II error have an inverse relationship.

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

A: Numerical Descriptive Techniques

B: Numerical Descriptive Techniques

C: Numerical Descriptive Techniques

Data Collection and Sampling

Probability

A: Random Variables and Discrete Probability Distributions

B: Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Estimation

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests

A: Simple Linear Regression and Correlation

B: Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Statistics

Time-Series Analysis and Forecasting

Statistical Process Control

Decision Analysis

Conclusion

Filters

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

A sample is used to obtain a 95% confidence interval for the mean of a population.The confidence interval goes from 10.89 to 13.21.If the same sample had been used to test H₀: $\mu$ = 12 vs.H₁: $\mu$ $\neq$ 12,H₀ could not be rejected at the 0.05 level.

A two-tail test for the population mean $\mu$ produces a test-statistic z = 1.89.The p-value associated with the test is 0.0588.

In testing the hypotheses H₀: $\mu$ = 50 vs.H₁: $\mu$ < 50,we found that the standardized test statistic is z = -1.59.Calculate the p-value,and state your conclusion if $\alpha$ = .025.