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Chapter 9: Q.19 (page 537)

A microbiologist is testing a water sample for E-coli. Suppose the null hypothesis, H0, is: the sample does not contain E-coli. The probability that the sample does not contain E-coli, but the microbiologist thinks it does is 0.012. The probability that the sample does contain E-coli, but the microbiologist thinks it does not is 0.002. What is the power of this test?

Short Answer

Expert verified

ff

Step by step solution

01

step1:

Ho: The sample is free of E. coli.

The chance that the sample does not contain E. coli but that the microbiologist believes it does 0.012.

The chance that the sample contains E. coli but the microbiologist does not believes it does is 0.002.

02

step2:

A test's power is 1-β, where ß is the probability of making a type I error.

03

s

We have

Type I error based on the information provided: the sample does not contain E. coli, but the microbiologist believes it does.

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Most popular questions from this chapter

The mean throwing distance of a football for Marco, a high school freshman quarterback, is 40yards, with a standard deviation of two yards. The team coach tells Marco to adjust his grip to get more distance. The coach records the distances for 20throws. For the 20throws, Marco’s mean distance was 45yards. The coach thought the different grip helped Marco throw farther than 40yards. Conduct a hypothesis test using a preset α=0.05. Assume the throw distances for footballs are normal.

First, determine what type of test this is, set up the hypothesis test, find thep-value, sketch the graph, and state your conclusion.

Previously, an organization reported that teenagers spent 4.5hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75hours with a sample standard deviation of 2.0. Conduct a hypothesis test.

At a significance level of a=0.05, what is the correct conclusion?

a. There is enough evidence to conclude that the mean number of hours is more than4.75

b. There is enough evidence to conclude that the mean number of hours is more than 4.5

c. There is not enough evidence to conclude that the mean number of hours is more than 4.5

d. There is not enough evidence to conclude that the mean number of hours is more than 4.75

Instructions: For the following ten exercises,

Hypothesis testing: For the following ten exercises, answer each question.

a. State the null and alternate hypothesis.

b. State the p-value.

c. State alpha.

d. What is your decision?

e. Write a conclusion.

f. Answer any other questions asked in the problem

"Japanese Girls’ Names"

by Kumi Furuichi

It used to be very typical for Japanese girls’ names to end with “ko.” (The trend might have started around my

grandmothers’ generation and its peak might have been around my mother’s generation.) “Ko” means “child” in Chinese characters. Parents would name their daughters with “ko” attaching to other Chinese characters which have meanings that they want their daughters to become, such as Sachiko—happy child, Yoshiko—a good child, Yasuko—a healthy child, and so on.

However, I noticed recently that only two out of nine of my Japanese girlfriends at this school have names which end with “ko.” More and more, parents seem to have become creative, modernized, and, sometimes, westernized in naming their children.

I have a feeling that, while 70 percent or more of my mother’s generation would have names with “ko” at the end,

the proportion has dropped among my peers. I wrote down all my Japanese friends’, ex-classmates’, co-workers, and

acquaintances’ names that I could remember. Following are the names. (Some are repeats.) Test to see if the proportion has

dropped for this generation.

Ai, Akemi, Akiko, Ayumi, Chiaki, Chie, Eiko, Eri, Eriko, Fumiko, Harumi, Hitomi, Hiroko, Hiroko, Hidemi, Hisako,

Hinako, Izumi, Izumi, Junko, Junko, Kana, Kanako, Kanayo, Kayo, Kayoko, Kazumi, Keiko, Keiko, Kei, Kumi, Kumiko,

Kyoko, Kyoko, Madoka, Maho, Mai, Maiko, Maki, Miki, Miki, Mikiko, Mina, Minako, Miyako, Momoko, Nana, Naoko,

Naoko, Naoko, Noriko, Rieko, Rika, Rika, Rumiko, Rei, Reiko, Reiko, Sachiko, Sachiko, Sachiyo, Saki, Sayaka, Sayoko,

Sayuri, Seiko, Shiho, Shizuka, Sumiko, Takako, Takako, Tomoe, Tomoe, Tomoko, Touko, Yasuko, Yasuko, Yasuyo, Yoko, Yoko, Yoko, Yoshiko, Yoshiko, Yoshiko, Yuka, Yuki, Yuki, Yukiko, Yuko, Yuko.

Driver error can be listed as the cause of approximately 54%of all fatal auto accidents, according to the American Automobile Association. Thirty randomly selected fatal accidents are examined, and it is determined that 14were caused by driver error. Using α=0.05, is the AAA proportion accurate?

Draw the graph of a two-tailed test.
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