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Exam 11: Introduction to Hypothesis Testing

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Question 91

True/False

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It is possible to commit a Type I error and a Type II error at the same time.

A) True
B) False

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Question 92

Multiple Choice

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In order to determine the p-value,which of the following is not needed?

A) The level of significance.
B) Whether the test is one-tail or two-tail.
C) The value of the test statistic.
D) All of these choices are true.

E) B) and C)
F) All of the above

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Question 93

Multiple Choice

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Which of the following would be an appropriate alternative hypothesis?

Using the confidence interval when conducting a two-tail test for the population mean μ,we do not reject the null hypothesis if the hypothesized value for μ falls between the lower and upper confidence limits.

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

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

Marathon Runners A researcher wants to study the average miles run per day for marathon runners.In testing the hypotheses: H₀: μ = 25 miles vs.H₁: μ ≠ 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.

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

Rechargeable Batteries A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours).In testing the hypotheses,H₀: μ = 950 hours vs.H₁: μ ≠ 950 hours,a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours. ​ ​ -{Rechargeable Batteries Narrative} Calculate β,the probability of a Type II error when μ = 1000 and α = 0.10.

If the probability of committing a Type I error for a given test is decreased,then for a fixed sample size n,the probability of committing a Type II error will:

Which of the following probabilities is equal to the significance level α?

A one-tail test for the population mean μ produces a test-statistic z = −0.75.The p-value associated with the test is 0.7734.

When a null hypothesis is rejected,the test is said to be statistically ____________________ at level α.

For a given level of significance,if the sample size increases,the probability of a Type II error will:

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

The numerical quantity computed from the data that is used in deciding whether to reject H₀ is the:

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

Rechargeable Batteries A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours).In testing the hypotheses,H₀: μ = 950 hours vs.H₁: μ ≠ 950 hours,a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours. ​ ​ -{Rechargeable Batteries Narrative} Calculate the power of the test when μ = 1000 and α = 0.10.

The ____________________ is a measure of the amount of statistical evidence that supports the alternative hypothesis.

The critical values zα or zα _{/ 2} are the boundary values for: