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Chapter 9: Q 96. (page 610)

Preventing colds A medical experiment investigated whether taking the herb echinacea could help prevent colds. The study measured 50 different response variables usually associated with colds, such as low-grade fever, congestion, frequency of coughing, and so on. At the end of the study, those taking echinacea displayed significantly better responses at the伪=0.05 level than those taking a placebo for 3 of the 50 response variables studied. Should we be convinced that echinacea helps prevent colds? Why or why not?

Short Answer

Expert verified

There isn't enough evidence to establish that Echinacea is helpful in preventing colds.

Step by step solution

01

Given information

伪=0.05

02

Calculation

To conclude that Echinacea is useful, there is insufficient evidence. The substantial results for the three variables are almost certainly coincidental.

When the null hypothesis is true 5%of the time, there is a type Ierror getting a significant result at the 伪=0.05level.

If 50t鈭�tests are run at this level of significance and all 50null hypotheses are true, the average Type Ierror is 0.05脳50=2.5

The three most important findings Such errors are very likely to occur in this setting.

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Most popular questions from this chapter

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^

Home computersRefer to Exercise 35.

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

b. Calculate the standardized test statistic and P-value.

c. What conclusion would you make?

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.

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 鈥攁ll of which would be classified as bullying. Do these data provide convincing evidence at the 伪=0.05significance level that the media report鈥檚 claim is correct?

Potato power problems Refer to Exercises 85 and 87

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 500 potatoes instead of 250 potatoes from the shipment.
See all solutions

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