Exam 11: Introduction to Hypothesis Testing

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} State the appropriate null and alternative hypotheses.

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

Toaster Oven An appliance manufacturer claims to have developed a new toaster oven that consumes an average of no more than 250 W.From previous studies, it is believed that power consumption for toaster ovens is normally distributed with a standard deviation of 18 W.A consumer group suspects the actual average is more than 250 W.They take a sample of 20 toaster ovens and calculate the average consumption to be 260 W. -{Toaster Oven Narrative} What is the conclusion from the hypothesis test using $\alpha$ = .05?

An alternative or research hypothesis is an assertion that holds if the null hypothesis is false.

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

If we do not reject the null hypothesis, we conclude that there ____________________(is/is not) enough statistical evidence to infer that the alternative hypothesis is true.

The probability of a Type I error is denoted by:

In order to determine the p-value, it is necessary to know the level of significance.

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?

We have created a 90% confidence interval for $\mu$ with the result (25, 32).What conclusion will we make if we test H₀: $\mu$ = 28 vs.H₁: $\mu$ $\neq$ 28 at $\alpha$ = 0.10?

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

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 p-value.

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} Using a standardized test statistic, test the hypothesis at the 5% level of significance if the sample mean filling weight is 48.6 ounces.

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

The probability of making a Type I error and the level of significance are the same.

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

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 value of the test statistic and set up the rejection region at the 0.025 level.What is your conclusion?

The p-value of a test is the:

Suppose that we reject a null hypothesis at the 0.05 level of significance.Then for which of the following $\alpha$ -values do we also reject the null hypothesis?

The owner of a local Karaoke Bar has recently surveyed a random sample of n = 300 customers of the bar.She would now like to determine whether or not the mean age of her customers is over 35.If so, she plans to alter the entertainment to appeal to an older crowd.If not, no entertainment changes will be made.If she wants to be 99% confident in her decision, what rejection region she use if the population standard deviation $\sigma$ is known?