Question

Water specimens are taken from water used for cooling as it is being discharged from a power plant into a river. It has been determined that as long as the mean temperature of the discharged water is at most 150°F, there will be no negative effects on the river's ecosystem. To investigate whether the plant is in compliance with regulations that prohibit a mean discharge water temperature above 150°F, researchers will take 50 water specimens at randomly selected times and record the temperature of each specimen. The resulting data will be used to test the hypotheses

H₀: μ = 150°F

versus

H_a: μ > 150°F.

(a) In the context of this example, describe Type I and Type II errors. (Select all that apply.)

A Type I error is not obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is greater than 150°F.

A Type I error is obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is (at most) 150°F.

A Type II error is obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is (at most) 150°F.

A Type II error is not obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is greater than 150°F.

A magazine collects data each year on the price of a hamburger in a certain fast food restaurant in various countries around the world. The price of this hamburger for a sample of restaurants in Europe in January resulted in the following hamburger prices (after conversion to U.S. dollars).

5.17	4.93	4.09	4.67	5.22	4.69
4.15	4.97	5.13	5.53	5.36	4.60

The mean price of this hamburger in the U.S. in January was $4.61. For purposes of this exercise, assume it is reasonable to regard the sample as representative of these European restaurants. Does the sample provide convincing evidence that the mean January price of this hamburger in Europe is greater than the reported U.S. price? Test the relevant hypotheses using

α = 0.05.

(Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

t	=
P-value	=

Medical research has shown that repeated wrist extension beyond 20 degrees increases the risk of wrist and hand injuries. Each of 24 students at a university used a proposed new computer mouse design. While using the mouse, each student's wrist extension was recorded. Data consistent with summary values given in a paper are given. Use these data to test the hypothesis that the mean wrist extension for people using this new mouse design is greater than 20 degrees. (Use

α = 0.05.

Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

26	28	25	27	26	24	24	25	25	25	24	28
22	24	25	28	26	27	31	24	28	26	26	24

t	=
P-value	=

Answer 1

Explanation : Type I error is probability of rejecting null when it is actually true. Type II error is accepting null when it is actually False. Above answers are obtained from this definitions.

2.

3

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