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Chapter 9: Q T9.4 (page 616)

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.

Short Answer

Expert verified

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

Step by step solution

01

Step 1:Given information

A significance test allows you to reject a null hypothesis H0H0in favor of an alternative hypothesis HaHaat the5% significance level.

02

Step 2:Explaination

Reject the null hypothesis }H0if and only if and given that the P-value is smaller than the significance level.

At the 5 percent significance level the null hypothesis was rejected:

P<0.05=5%

Do not know if the p-valuePis less than1%or not

Hence, the correct option is (e)

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Most popular questions from this chapter

A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of 1 inch could be increased by

a. using only volunteers from the basketball team in the experiment.

b. usingα=0.05 instead of α=0.05

c. using α=0.05instead of α=0.01

d. giving the drug to 25 randomly selected students instead of 50.

e. using a two-sided test instead of a one-sided test.

Pressing pills Refer to Exercise 77.

a. Construct and interpret a 95% confidence interval for the true hardness μ 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.

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?

Packaging DVDs (6.2,5.3) A manufacturer of digital video discs (DVDs) wants to be sure that the DVDs will fit inside the plastic cases used as packaging. Both the cases and the DVDs are circular. According to the supplier, the diameters of the plastic cases vary Normally with mean μ=5.3inches and standard deviation σ=0.01inch. The DVD manufacturer produces DVDs with mean diameterμ=5.26inches. Their diameters follow a Normal distribution with σ=0.02inch.

a. Let X = the diameter of a randomly selected case and Y = the diameter of a randomly selected DVD. Describe the shape, center, and variability of the distribution of the random variable X−Y. What is the importance of this random variable to the DVD manufacturer?

b. Calculate the probability that a randomly selected DVD will fit inside a randomly selected case.

c. The production process runs in batches of 100 DVDs. If each of these DVDs is paired with a randomly chosen plastic case, find the probability that all the DVDs fit in their cases.

A company that manufactures classroom chairs for high school students

claims that the mean breaking strength of the chairs is 300 pounds. One of the chairs collapsed beneath a 220-pound student last week. You suspect that the manufacturer is exaggerating the breaking strength of the chairs, so you would like to perform a test of H0:μ=300Ha:μ<300where μ is the true mean breaking strength of this company’s classroom chairs.

a. The power of the test to detect that μ=294 based on a random sample of 30

chairs and a significance level of α=0.05 is 0.71. Interpret this value.

b. Find the probability of a Type I error and the probability of a Type II error for the test in part (a).

c. Describe two ways to increase the power of the test in part (a).
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