Exam 11: Introduction to Hypothesis Testing

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.

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

To increase the power of a test, ____________________ the sample size.

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

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

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

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

Think about a situation where you have a test for a virus.First, you are tested positive or negative.Second, you either really do have the virus or you don't. a. If you actually have the virus but the test did not catch it, which error has been made and what is the impact of that error? b. If you actually don't have the virus but the test says you did, which error is being made and what is the impact of this error? c. Which error is the worst one to commit in this situation and why?

A Type I error is represented by $\beta$ .

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 parameter of interest in this situation?

Which of the following would be an appropriate alternative hypothesis?

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 $\beta$ ?

For a given sample size, the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced.

During the last energy crisis, a government official claimed that the average car owner refills the tank when there is more than 3 gallons left.To check the claim, 10 cars were surveyed as they entered a gas station.The amount of gas remaining before refill was measured and recorded as follows (in gallons): 3, 5, 3, 2, 3, 3, 2, 6, 4, and 1.Assume that the amount of gas remaining in tanks is normally distributed with a standard deviation of 1 gallon.Compute the probability of a Type II error and the power of the test if the true average amount of gas remaining in tanks is 3.5 gallons anda= 0.10.

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?

If a researcher rejects a true null hypothesis, she has made a(n) ____________________ error.

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} Calculate $\beta$ , the probability of a Type II error when $\mu$ = 1000 and $\alpha$ = 0.10.

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

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} Calculate the power of the test when $\mu$ = 1000 and $\alpha$ = 0.10.

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