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Chapter 9: Q 20. (page 565)

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.

Short Answer

Expert verified

The data do not show that H1is true, it show that alternative hypothesis H1is true.

Step by step solution

01

Given Information

It is given that p=0.01

伪=0.05

H0:渭=12

H1:渭鈮�12

02

Explanation

As 0.01<0.05鈬�RejectH0

There is convincing evidence that null hypothesis is not true.

Issue with statement is:

  • Data do not convince that H1is true.
  • It shows that alternative hypothesisH1is true.

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Most popular questions from this chapter

Teen drivers Refer to Exercise 51.

a. Construct and interpret a 95% confidence interval for the true proportion p of all teens in the state who passed their driving test on the first attempt. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) provides more information than the test in Exercise 51.

Do you Tweet? The Pew Internet and American Life Project asked a random sample of U.S. adults, 鈥淒o you ever 鈥� use Twitter or another service to share updates about yourself or to see updates about others?鈥� According to Pew, the resulting 95% confidence interval is (0.123, 0.177).11 Based on the confidence interval, is there convincing evidence that the true proportion of U.S. adults who would say they use Twitter or another service to share updates differs from 0.17? Explain your reasoning.

Restaurant power problems Refer to Exercises 86 and 88

a. Explain one disadvantage of using 伪=0.10 instead of 伪=0.05 when

performing the test.

b. Explain one disadvantage of taking a random sample of 50 people instead of 30 people.

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

Error probabilities and power You read that a significance test at the 伪=0.01

significance level has probability 0.14of making a Type II error when a specific alternative is true.

a. What is the power of the test against this alternative?

b. What鈥檚 the probability of making a Type I error?
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