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Chapter 9: Q 105. (page 611)

After checking that conditions are met, you perform a significance test of H0:渭=1versus Ha:渭鈮�1You obtain a P-value of 0.022Which of the following must be true?

a. A 95%confidence interval for 渭渭 will include the value 1

b. A 95%confidence interval for 渭渭 will include the value 0.022

c. A 99%confidence interval for 渭渭 will include the value1

d. A 99%confidence interval for 渭渭 will include the value 0.022

e. None of these is necessarily true.

Short Answer

Expert verified

The correct option is (c) A 99% confidence interval for 渭渭 will include the value 1

Step by step solution

01

Given information

H0:渭=1Ha:渭鈮�1P=0.022

02

Calculation

The null hypothesis is rejected if the P-value is less than the significance level.

P<0.05=5%rejectH0P>0.01=1%=failstorejectH0

A significance test at the 5% significance level equates to a 95 percent confidence interval.

A significance test at the 1% significance level equates to a 99 percent confidence interval.

There is no one in 95% of the confidence interval.

There are 1 in the 95% confidence interval.

So correct option is (c).

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Most popular questions from this chapter

Teens and sex The Gallup Youth Survey asked a random sample of U.S. teens aged 13 to 17 whether they thought that young people should wait until marriage to have sex.14 The Minitab output shows the results of a significance test and a 95% confidence interval based on the survey data.

a. Define the parameter of interest.

b. Check that the conditions for performing the significance test are met in this case.

c. Interpret the P-value.

d. Do these data give convincing evidence that the actual population proportion differs from 0.5? Justify your answer with appropriate evidence.

Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of 10 mice takes with a loud noise as stimulus. The appropriate hypotheses for the significance test are

a. H0:渭=18;Ha:渭鈮�18

b. H0:渭=18;Ha:渭>18

c. H0:渭<18;Ha:渭=18

d. H0:渭=18;Ha:渭<18

e. H0:x炉=18;Ha:x炉<18

Explaining confidence: Here is an explanation from a newspaper concerning one of its opinion polls. Explain what is wrong with the following statement.

For a poll of 1600 adults, the variation due to sampling error is no more than 3

percentage points either way. The error margin is said to be valid at the 95%

confidence level. This means that, if the same questions were repeated in 20 polls, the results of at least 19 surveys would be within 3 percentage points of the results of this survey.

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

Calculations and conclusions Refer to Exercise R9.1. Find the standardized test statistic and P-value in each setting, and make an appropriate conclusion.
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