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Exam 11: Introduction to Hypothesis Testing

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Question 41

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To test the hypotheses: H₀: $\mu$ = 40 vs.H₁: $\mu$ $\neq$ 40,we draw a random sample of size 16 from a normal population whose standard deviation is 5.If we set $\alpha$ = 0.01,find the probability of committing a Type II error when $\mu$ = 37.

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= P(36.775 < < 43....

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Question 42

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A(n)____________________ characteristic curve plots the probability of a Type II error for various alternative values of ____________________.

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Question 43

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If the p value is less than $\alpha$ in a two-tail test:

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?

As the alternative value of $\mu$ increases,so does the power of the test.

In a two-tail test for the population mean,if the null hypothesis is rejected when the alternative hypothesis is true:

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

It is possible to commit a Type I error and a Type II error at the same time.

You reject H₀ if the p-value of your hypothesis is ____________________ than the significance level.

If we reject the null hypothesis when it is false,then we have committed:

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

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

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?

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 hypothesis testing procedure begins with the assumption that the null hypothesis is ____________________.

In a one-tail test,the p-value is found to be equal to 0.054.If the test had been two-tail,then the p-value would have been 0.027.

If we reject the null hypothesis,we conclude that there is enough statistical evidence to infer that the alternative hypothesis is true.

A Type I error occurs when we:

A Type II error is defined as: