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Chapter 9: Q .13. (page 564)

Interpreting a P-value A student performs a test of H0:渭=100H0:渭=100versus Ha: 渭>100Ha:渭>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:渭=100H0:渭=100versusHa:渭>100Ha:渭>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:渭=100

Ha:渭>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

A milk processor monitors the number of bacteria per milliliter in raw milk received at the factory. A random sample of 10one-milliliter specimens of milk supplied by one producer gives the following data:

Construct and interpret a 90% confidence interval for the population mean 渭.

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a. Define the parameter of interest.

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

Awful accidents Slow response times by paramedics, firefighters, and policemen can have serious consequences for accident victims. In the case of life-threatening injuries, victims generally need medical attention within 8minutes of the accident. Several cities have begun to monitor emergency response times. In one such city, emergency personnel took more than 8minutes to arrive on 22%of all calls involving life-threatening injuries last year. The city manager shares this information and encourages these first responders to 鈥渄o better.鈥� After 6months, the city manager selects an SRS of 400 calls involving life- threatening injuries and examines the response times. She then performs a test at the 伪=0.05level of H0: p=0.22versus Ha:p<0.22, where pis the true proportion of calls involving life-threatening injuries during this 6-month period for which emergency personnel took more than 8minutes to arrive.

a. Describe a Type I error and a Type II error in this setting.

b. Which type of error is more serious in this case? Justify your answer.

c. Based on your answer to part (b), do you agree with the manager鈥檚 choice of 伪=0.05? Why or why not?

Walking to school Refer to Exercise 36.

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

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c. What conclusion would you make?

Clean water The Environmental Protection Agency (EPA) has determined that safe

drinking water should contain at most 1.3mg/liter of copper, on average. A water supply company is testing water from a new source and collects water in small bottles at each of30randomly selected locations. The company performs a test at the 伪=0.05 significance level ofH0:渭=1.3versus Ha:渭>1.3, where 渭 is the

true mean copper content of the water from the new source.

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