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Chapter 9: Q 90. (page 609)

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.

Short Answer

Expert verified

Part (a) There is the most likely to have a type I error.

Part (b) There is more time consuming and costly to collect the data.

Step by step solution

01

Part (a) Step 1: Given information

伪=0.05H0:渭=$85,000渭>$85,000渭=$86,000
02

Part (a) Step 2: Explanation

Type I error: Reject the null hypothesis H0, once the null hypothesis H0is true.

伪Showing the probability of a type I error.

If you increase 伪=0.05to伪=0.10 the likelihood of making a type I error increases, and you're more likely to make one, which is a negative.

03

Part (b) Step 1: Explanation

If the sample size is increased from 30to 50persons, collecting data for the 50people will take longer and cost more money than collecting data for the 30people (as there are about twice as many potatoes about which we need to gather information.).

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Most popular questions from this chapter

Reality TVTelevision networks rely heavily on ratings of TV shows when deciding

whether to renew a show for another season. Suppose a network has decided that

鈥淢iniature Golf with the Stars鈥� will only be renewed if it can be established that more than 12%of U.S. adults watch the show. A polling company asks a random sample of 2000U.S. adults if they watch 鈥淢iniature Golf with the Stars.鈥� The network uses the data to perform a test of

H0:p=0.12

Ha:p>0.12

where pis the true proportion of all U.S. adults who watch the show. Describe a Type Ierror and a TypeIIerror in this setting, and give a possible consequence of each.

Pressing pills A drug manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each batch of tablets produced is measured to control the compression process. The target value for the hardness is 渭=11.5The hardness data for a random sample of 20 tablets from one large batch are

Is there convincing evidence at the 5%level that the mean hardness of the tablets in this batch differs from the target value?

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^

How much juice? Refer to Exercise 3. The mean amount of liquid in the bottles is 179.6ml and the standard deviation is 1.3ml. A significance test yields a P-value of 0.0589. Interpret the P-value.

A significance test allows you to reject a null hypothesis H0H0in favor of an alternative hypothesisHaaat the 5%significance level. What can you say about significance at the1%level?

a.H0H0can be rejected at the1%significance level.

b. There is insufficient evidence to rejectH0H0at the1%significance level.

c. There is sufficient evidence to accept H0H0at the 1%significance level.

d.HaHacan be rejected at the 1%significance level.

e. The answer can't be determined from the information given.
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