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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

Water! A blogger claims that U.S. adults drink an average of five 8-ounce glasses (that鈥檚 40 ounces) of water per day. Researchers wonder if this claim is true, so they ask a random sample of 24 U.S. adults about their daily water intake. A graph of the data shows a roughly symmetric shape with no outliers.

a. State an appropriate pair of hypotheses for a significance test in this setting. Be sure to define the parameter of interest.

b. Check conditions for performing the test in part (a).

c. The 90% confidence interval for the mean daily water intake is 30.35 to 36.92 ounces. Based on this interval, what conclusion would you make for a test of the hypotheses in part (a) at the 10% significance level?

d. Do we have convincing evidence that the amount of water U.S. children drink per day differs from 40 ounces? Justify your answer.

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

A government report says that the average amount of money spent per U.S. household per week on food is about \(158. A random sample of50 households in a small city is selected, and their weekly spending on food is recorded. The sample data have a mean of \)165 and a standard deviation of \(20. Is there convincing evidence that the mean weekly spending on food in this city differs from the national figure of \)158?

Watching grass grow The germination rate of seeds is defined as the proportion of seeds that sprout and grow when properly planted and watered. A certain variety of grass seed usually has a germination rate of 0.80. A company wants to see if spraying the seeds with a chemical that is known to increase germination rates in other species will increase the germination rate of this variety of grass. The company researchers spray a random sample of 400grass seeds with the chemical, and 339of the seeds germinate. Do these data provide convincing evidence at the 伪=0.05 significance level that the chemical is

effective for this variety of grass?

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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