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Chapter 9: Q .2. (page 563)

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

Short Answer

Expert verified

H0:p=72%=0.72

H0:p=72%=0.72

Step by step solution

01

Step 1:Given information

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

02

Step 2:Explaination

Claim is proportion is72%.

The null hypothesis statement is that the population value is equal to the value given in the claim:

H0:p=72%=0.72

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population proportion is equal to the value given in the claim. If the null hypothesis is the claim, then the alternative hypothesis statement would be the opposite of the null hypothesis.

Ha:p鈮�0.72

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Most popular questions from this chapter

Don鈥檛 argue Refer to Exercises 2 and 12.

a. What conclusion would you make at the 伪=0.01 level?

b. Would your conclusion from part (a) change if a 5% significance level was used

instead? Explain your reasoning.

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.

1 A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay \(100 for the upgrade. For the upgrade to be profitable, the company must sell it to more than 20% of their customers. You contact a random sample of 60 customers and find that 16 would be willing to pay \)100 for the upgrade.

a. Do the sample data give convincing evidence that more than 20% of the company鈥檚 customers are willing to purchase the upgrade? Carry out an appropriate test at the 伪=0.05significance level.

b. Which would be a more serious mistake in this setting鈥攁 Type I error or a Type II error? Justify your answer.

c. Suppose that 30% of the company鈥檚 customers would be willing to pay $100 for the upgrade. The power of the test to detect this fact is0.60. Interpret this value.

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

Powerful potatoes Refer to Exercise 85. Determine if each of the following

changes would increase or decrease the power of the test. Explain your answers.

a. Change the significance level to 伪=0.10

b. Take a random sample of 250 potatoes instead of 500 potatoes.

c. The true proportion is p=0.10 instead of p=0.11
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