Chapter 9: Q T9.8 (page 616)
In a test ofagainst , a random sample of size 100 yields a standardized test statistic of . Which of the following is closest to the P-value for this test?
a. 0.90
b. 0.40
c. 0.05
d. 0.20
e. 0.10
The correct option is (d) i.e
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Error probabilities and power You read that a significance test at the
significance level has probability of making a Type II error when a specific alternative is true.
a. What is the power of the test against this alternative?
b. What’s the probability of making a Type I error?
Reporting cheating What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of 172 undergraduates at a large university: “You witness two students cheating on a quiz. Do you go to the professor?” The Minitab output shows the results of a significance test and a 95% confidence interval based on the survey data.13
a. Define the parameter of interest.
b. Check that the conditions for performing the significance test are met in this case.
c. Interpret the P-value.
d. Do these data give convincing evidence that the population proportion differs from ? Justify your answer with appropriate evidence.
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 The hardness data for a random sample of 20 tablets from one large batch are
Is there convincing evidence at the level that the mean hardness of the tablets in this batch differs from the target value?
Tests and confidence intervals The P-value for a two-sided test of the null hypothesis
a. Does the confidence interval for include ? Why or why not?
b. Does the confidence interval for include ? Why or why not?
Based on the -value in Exercise 31, which of the following would be the most
appropriate conclusion?
a. Because the P-value is large, we reject . We have convincing evidence that more than of city residents support the tax increase.
b. Because the -value is large, we fail to reject . We have convincing evidence that more than of city residents support the tax increase.
c. Because the -value is large, we reject . We have convincing evidence that at most of city residents support the tax increase.
d. Because the -value is large, we fail to reject . We have convincing evidence that at most of city residents support the tax increase.
e. Because the -value is large, we fail to reject . We do not have convincing
evidence that more than of city residents support the tax increase.
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