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Chapter 9: Q 86. (page 608)

Upscale restaurant You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over \(85,000to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50people living near one potential site. Based on the mean income of this sample, you will perform a test at the

伪=0.05 significance level of H0:渭=\)85,000versus Ha:渭>\(85,000, where 渭 is the true mean income in the population of people who live near the restaurant. The power of the test to detect that 渭=\)86,000is 0.64 Interpret this value.

Short Answer

Expert verified

There is 64 percent probability that finds the convincing proof to help the alternative hypothesis渭>$85000

Step by step solution

01

Given information

H0:渭=$85000H1:渭>$85000渭A=alternativemean=$86000

伪=significancelevel=0.05

Power =0.64=64%

02

Concept

When the alternative hypothesis is true, the power is the probability of rejecting the null hypothesis.

03

Explanation

If the genuine mean income in the population of persons who live near the restaurant is $86000 there is a 64 percent chance that the alternative hypothesis 渭>$85000 will be supported.

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Most popular questions from this chapter

An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are

邪.H0:p鈭�=0.5;Ha:p鈭�>0.5H0:p^=0.5;Ha:p^>0.5.

b. H0:p=0.5;Ha:p>0.5H0:p=0.5;Ha:p>0.5.

c. H0:p=0.5;Ha:p<0.5H0:p=0.5;Ha:p<0.5.

d. H0:p=0.5;Ha:p鈮�0.H0:p=0.5;Ha:p鈮�0.5.

e. H0:p>0.5;Ha:p=0.5H0:p>0.5;Ha:p=0.5.

Don't argue! A Gallup poll report revealed that 72%of teens said they seldom or never argue with their friends. 3Yvonne wonders whether this result holds true in her large high school, so she surveys a random sample of 150students at her school.

state appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest

More lefties?In the population of people in the United States, about 10% are left-handed. After bumping elbows at lunch with several left-handed students, Simon wondered if more than 10%of students at his school are left-handed. To investigate, he selected an SRS of 50students and found 8lefties (p铃�=8/50=0.16).

To determine if these data provide convincing evidence that more than 10%of the students at Simon鈥檚 school are left-handed, 200trials of a simulation were conducted. Each dot in the graph shows the proportion of students that are left-handed in a random sample of 50students, assuming that each student has a 10%chance of being left handed.

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b. Use the simulation results to estimate the P-value of the test in part (a). Interpret the P-value.

c. What conclusion would you make?

Which of choices (a) through (d) is not a condition for performing a significance test about a population proportion p?

a. The data should come from a random sample from the population of interest.

b. Both np0and n(1-p0)should be at least 10.

c. If you are sampling without replacement from a finite population, then you should sample less than 10%of the population.

d. The population distribution should be approximately Normal unless the sample size is large.

e. All of the above are conditions for performing a significance test about a population proportion.

A random sample of 100 likely voters in a small city produced 59 voters in favor of Candidate A. The observed value of the standardized test statistic for performing a test of H0:p=0.5H0:p=0.5versus Ha:p>0.5Ha:p>0.5

is which of the following?

a)z=0.59-0.50.59(0.41)100

b)z=0.59-0.50.5(0.5)100

c)z=0.5-0.590.59(0.41)100

d)z=0.5-0.590.5(0.5)100

e)z=0.59-0.5100
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