Exam 11: Introduction to Hypothesis Testing

In a criminal trial,a Type I error is made when:

The level of significance can be:

In a criminal trial,a Type II error is made when:

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} Calculate the value of the test statistic.

A Type II error is represented by $\alpha$ ;it is the probability of rejecting a true null hypothesis.

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:

The p-value of a test is the smallest $\alpha$ at which the null hypothesis can be rejected.

A Type I error is represented by $\alpha$ ;it is the probability of rejecting a true null hypothesis.

You cannot commit a(n)____________________ error when the null hypothesis is true.

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?

After you set up the hypotheses and collect your data,you calculate the statistic that serves as the criterion for making your decision.This number is called the ____________________ statistic.

We cannot commit a Type I error when the:

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} Recalculate $\beta$ if $\alpha$ is lowered from 0.10 to 0.05.

LSAT Scores The Admissions officer for the graduate programs at the University of Pennsylvania believes that the average score on the LSAT exam at his university is significantly higher than the national average of 1,300.An accepted standard deviation for LSAT scores is 125.A random sample of 25 scores had an average of 1,375. -{LSAT Scores Narrative} Calculate the p-value.

The probability of a Type I error is denoted by ____________________.

As the sample size increases,the operating characteristic curves drop down to zero at a(n)____________________ rate.

Which of the following is an appropriate null hypothesis?

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} Set up the rejection region.

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} What can we conclude at the 5% significance level regarding the null hypothesis?

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