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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

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.

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 伪=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%?

Pressing pills Refer to Exercise 77.

a. Construct and interpret a 95% confidence interval for the true hardness 渭 of the tablets in this batch. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) is consistent with the result of the test in Exercise 77.

The standardized test statistic for a test of H0:p=0.4versus Ha:pnotequalto0.4isz=2.43This test is

a. not significant at either 伪=0.05or 伪=0.01

b. significant at 伪=0.05but not at伪=0.01

c. significant at伪=0.01but not at 伪=0.05

d. significant at both 伪=0.05and伪=0.01

e. inconclusive because we don鈥檛 know the value of p^

1 A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay \(100 for the upgrade. For the upgrade to be profitable, the company must sell it to more than 20% of their customers. You contact a random sample of 60 customers and find that 16 would be willing to pay \)100 for the upgrade.

a. Do the sample data give convincing evidence that more than 20% of the company鈥檚 customers are willing to purchase the upgrade? Carry out an appropriate test at the 伪=0.05significance level.

b. Which would be a more serious mistake in this setting鈥攁 Type I error or a Type II error? Justify your answer.

c. Suppose that 30% of the company鈥檚 customers would be willing to pay $100 for the upgrade. The power of the test to detect this fact is0.60. Interpret this value.
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