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Chapter 9: Q 35. (page 581)

Home computers Jason reads a report that says 80%of U.S. high school

students have a computer at home. He believes the proportion is smaller than 0.80at his large rural high school. Jason chooses an SRS of 60students and finds that 41have a computer at home. He would like to carry out a test at the 伪=0.05significance level of H0:p=0.80versus Ha:p<0.80, where p= the true

proportion of all students at Jason鈥檚 high school who have a computer at home. Check if the conditions for performing the significance test are met.

Short Answer

Expert verified

Yes, the conditions are fulfilled.

Step by step solution

01

Given Information

It is given that
(n)is60

(p)is0.80

H0:p=0.80

Ha:p<0.80

02

Checking the conditions

prefers to the proportion of students that own computer at home.

Conducting significance test, below conditions should be satisfied.

n脳p鈮�10

n脳(1-p)鈮�10

(1) n脳p=60脳0.8

=48>10

(2) n脳(1-p)=60脳(1-0.80)

=12>10

Both conditions are satisfied.

So, we can conduct significance test.

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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.

Making conclusions A student performs a test of H0:渭=12versus Ha:渭鈮�12

at the 伪=0.05significance level and gets a P-value of 0.01. The

student writes: 鈥淏ecause the P-value is small, we reject H0. The data prove that Hais true.鈥� Explain what is wrong with this conclusion.

Two-sided test Suppose you want to perform a test of H0:渭=64

versus Ha:渭notequalto64at the 伪=0.05significance level. A random sample

of size n=25 from the population of interest yields x炉=62.8 and sx=5.36

. Assume that the conditions for carrying out the test are met.

a. Explain why the sample result gives some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and P-value.

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

Jump around Student researchers Haley, Jeff, and Nathan saw an article on the Internet claiming that the average vertical jump for teens was 15 inches. They wondered if the average vertical jump of students at their school differed from 15 inches, so they obtained a list of student names and selected a random sample of 20 students. After contacting these students several times, they finally convinced them to allow their vertical jumps to be measured. Here are the data (in inches):

Do these data provide convincing evidence at the 伪=0.10 level that the average vertical jump of students at this school differs from 15 inches?
See all solutions

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