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Don't argue Refer to Exercise 2. Yvonne finds that 96 of the 150 students (64%) say they rarely or never argue with friends. A significance test yields a P-value of0.0291 Interpret the P-value.

Short Answer

Expert verified

There is a 2.91% possibility that the proportion of students in the sample who say they never argue with friends is0.64or more extreme, when the proportion of all students who say they never argue with friends is 0.72

Step by step solution

01

Step 1:Given information

Don't argue Refer to Exercise 2. Yvonne finds that96 of the 150students (64%) say they rarely or never argue with friends. A significance test yields a P-value of 0.0291

02

Step 2:Explaination

P=0.0291=2.91%

p^=64%=0.64

Claim is proportion is 72%

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

H0:p=72%=0.72

Ha:p0.72

The P-value is the probability of getting the value of the test static or a value more extreme, when the null hypothesis is correct.

There is a 2.91% possibility that the proportion of students in the sample who say they never argue with friends is0.64or more extreme, when the proportion of all students who say they never argue with friends is 0.72.

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Most popular questions from this chapter

Flu vaccine A drug company has developed a new vaccine for preventing the flu. The company claims that fewer than 5% of adults who use its vaccine will get the flu. To test the claim, researchers give the vaccine to a random sample of 1000 adults.

a. State appropriate hypotheses for testing the company鈥檚 claim. Be sure to define your parameter.

b. Describe a Type I error and a Type II error in this setting, and give the consequences Page Number: 615 of each.

c. Would you recommend a significance level of 0.01, 0.05, or 0.10 for this test? Justify your choice.

d. The power of the test to detect the fact that only 3% of adults who use this vaccine would develop flu using 伪=0.05 is 0.9437. Interpret this value.

e. Explain two ways that you could increase the power of the test from part (d).

Interpreting a P-value A student performs a test of H0:p=0.3H0:p=0.3versus Ha:p<0.3Ha:p<0.3and gets a P-value of 0.22The student says, "This means there is about a22%chance that the null hypothesis is true." Explain why the student's explanation is wrong.

We want to be rich In a recent year, 73%of first-year college students responding to a national survey identified 鈥渂eing very well-off financially鈥 as an important personal goal. A state university finds that 132of an SRS of 200of its first-year students say that this goal is important. Is there convincing evidence at the =0.05significance level that the proportion of all first-year students at this university who think being very well-off is important differs from the national value of 73%?

Home computersRefer to Exercise 35.

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

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

c. What conclusion would you make?

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 =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.

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