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Chapter 9: Q .13. (page 564)

Interpreting a P-value A student performs a test of H0:μ=100H0:μ=100versus Ha: μ>100Ha:μ>100and gets a P-value of 0.044.The student says, "There is a0.044 probability of getting the sample result I did by chance alone." Explain why the student's explanation is wrong.

Short Answer

Expert verified

- The interpretation is not given that the probability only carries when the null hypothesis is true.

- The interpretation is not given that the sample results can be more extreme (larger) as well.

Step by step solution

01

Step 1:Given information

Interpreting a P-value A student performs a test of $H0:μ=100H0:μ=100versusHa:μ>100Ha:μ>100and gets a P-value of0.044. The student says, "There is a0.044probability of getting the sample result I did by chance alone."

02

Step 2:Explaianation

P=0.044=4.4%

H0:μ=100

Ha:μ>100

The p-value is the probability of getting the value of the test statistic, or a value more extreme, when the null hypothesis is true.

It is observed that there are two issues with the given interpretation of the P-value:

- The interpretation is not given that the probability only carries when the null hypothesis is true.

- The interpretation is not given that the sample results can be more extreme (larger) as well.

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Most popular questions from this chapter

18%Members of the city council want to know if a majority of city residents supports a 1%increase in the sales tax to fund road repairs. To investigate, they survey a random sample of 300city residents and use the results to test the following hypotheses:

H0:p=0.50

Ha:p>0.50

where pis the proportion of all city residents who support a 1%increase in the sales tax to fund road repairs.

In the sample, p^=158/300=0.527, The resulting P-value is 0.18. What is the correct interpretation of this P-value?

a. Only 18% of the city residents support the tax increase.

b. There is an 18%chance that the majority of residents supports the tax increase.

c. Assuming that 50%of residents support the tax increase, there is an 18%probability that the sample proportion would be 0.527or greater by chance alone.

d. Assuming that more than 50%of residents support the tax increase, there is an 18%probability that the sample proportion would be 0.527or greater by chance alone.

e. Assuming that 50%of residents support the tax increase, there is an 18% chance that the null hypothesis is true by chance alone.

Bullies in middle school A media report claims that more than 75%of

middle school students engage in bullying behavior. A University of Illinois study on aggressive behavior surveyed a random sample of 558middle school students. When asked to describe their behavior in the last 30days, 445students admitted that they had engaged in physical aggression, social ridicule, teasing, name-calling, and issuing threats —all of which would be classified as bullying. Do these data provide convincing evidence at the α=0.05significance level that the media report’s claim is correct?

Fire the coach!A college president says, “More than two-thirds of the alumni support my firing of Coach Boggs.” The president’s statement is based on 200emails he has received from alumni in the past three months. The college’s athletic director wants to perform a test of H0:p=2/3versus Ha:p>2/3, where p= the true proportion of the college’s alumni who favor firing the coach. Check if the conditions for performing the significance test are met.

You are testing H0:μ=10against Ha:μ<10based on an SRS of20

observations from a Normal population. The t statistic is t=−2.25

The P-value

a. falls between 0.01 and 0.02.

b. falls between 0.02 and 0.04.

c. falls between 0.04 and 0.05.

d. falls between 0.05 and 0.25.

e. is greater than 0.25.

Stating hypotheses

a. A change is made that should improve student satisfaction with the parking situation at a local high school. Before the change, 37%of students approve of the parking that's provided. The null hypothesis H0:p>0.37H0:p>0.37is tested against the alternative Ha: p=0.37Ha:p=0.37

b. A researcher suspects that the mean birth weights of babies whose mothers did not see a doctor before delivery is less than 3000 grams. The researcher states the hypotheses as

H0:x-=3000grams-5H0:x¯=3000grams

Ha: x-<3000grams Ha:x¯<3000grams

explain what's wrong with the stated hypotheses. Then give correct hypotheses.
See all solutions

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