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Chapter 9: Q T9.10 (page 616)
Which of the following has the greatest probability?
a.if t has 5 degrees of freedom.
b. if t has 2 degrees of freedom.
c. if z is a standard Normal random variable.
d.if t has 5 degrees of freedom.
e. if z is a standard Normal random variable.
Option e)
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No homework? Mr. Tabor believes that less than of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of students at the school.
pg
No homework Refer to Exercises 1 and 9. What conclusion would you make at thelevel?
Flu vaccine A drug company has developed a new vaccine for preventing the flu. The company claims that fewer than 5% of adults who use its vaccine will get the flu. To test the claim, researchers give the vaccine to a random sample of 1000 adults.
a. State appropriate hypotheses for testing the company鈥檚 claim. Be sure to define your parameter.
b. Describe a Type I error and a Type II error in this setting, and give the consequences Page Number: 615 of each.
c. Would you recommend a significance level of 0.01, 0.05, or 0.10 for this test? Justify your choice.
d. The power of the test to detect the fact that only 3% of adults who use this vaccine would develop flu using 伪=0.05 is 0.9437. Interpret this value.
e. Explain two ways that you could increase the power of the test from part (d).
Teens and sex The Gallup Youth Survey asked a random sample of U.S. teens aged 13 to 17 whether they thought that young people should wait until marriage to have sex.14 The Minitab output shows the results of a significance test and a 95% confidence interval based on the survey data.
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 actual population proportion differs from ? Justify your answer with appropriate evidence.
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鈥檚 the probability of making a Type I error?
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