FiltersDone

Question type

Essay

Multiple Choice

Short Answer

True False

Matching

Exam 11: Introduction to Hypothesis Testing

Show Answer

Share

---

All types

Filters

Study FlashcardsPractice ExamLearn

Question 1

True/False

Review LaterAdd Note

Review Later

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

Correct Answer

verified

Show Answer

Question 2

True/False

Review LaterAdd Note

Review Later

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

Correct Answer

verified

Show Answer

Question 3

True/False

Review LaterAdd Note

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

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 $\beta$ ?

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

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.

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.

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

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

The power of a test is denoted by:

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

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

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

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:

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.

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

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.

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

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.

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.