Exam 11: Introduction to Hypothesis Testing

One way of expressing how well a test performs is to report its power--the probability of detecting a false null hypothesis.

In testing the hypotheses H₀: $\mu$ = 50 vs.H₁: $\mu$ $\neq$ 50,the following information is known: n = 64, $\bar { x }$ = 53.5,and $\sigma$ = 10.The standardized test statistic z equals:

In testing the hypotheses H₀: $\mu$ = 75 vs.H₁: $\mu$ < 75,if the value of the test statistic z equals -2.42,then the p-value is:

Which of the following probabilities is equal to the significance level $\alpha$ ?

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 power of a test is the probability that a true null hypothesis will be rejected.

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 value of the test statistic?

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} Interpret the meaning of the power of the test.

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} Explain briefly how to use the confidence interval to test the hypothesis.

Which of the following would be an appropriate alternative hypothesis?

Researchers claim that 40 tissues is the average number of tissues a person uses during the course of a cold.The company who makes Puffs brand tissues thinks that fewer of their tissues are needed.What are their null and alternative hypotheses?

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

A Type II error is represented by $\beta$ ;it is the probability of failing to reject a false null hypothesis.

The owner of a local Jazz Club has recently surveyed a random sample of n = 200 customers of the club.She would now like to determine whether or not the mean age of her customers is over 30.If so,she plans to alter the entertainment to appeal to an older crowd.If not,no entertainment changes will be made.The appropriate hypotheses to test are:

To calculate the probability of a(n)____________________ error you need to specify a value of $\mu$ other than the one given in the null hypothesis.

If we reject a null hypothesis at the 0.05 level of significance,then we must also reject it at the 0.10 level.

If we do not reject the null hypothesis,we conclude that:

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

For a given level of significance,if the sample size is increased,the power of the test will ____________________.

When a null hypothesis is rejected,the test is said to be statistically ____________________ at level $\alpha$ 0.