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Chapter 9: Q. 61. (page 584)
The standardized test statistic for a test of versus isThis test is
a. not significant at either or
b. significant at but not at
c. significant atbut not at
d. significant at both and
e. inconclusive because we don鈥檛 know the value of
The test is significant at and
The correct option is
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Awful accidents Slow response times by paramedics, firefighters, and policemen can have serious consequences for accident victims. In the case of life-threatening injuries, victims generally need medical attention within minutes of the accident. Several cities have begun to monitor emergency response times. In one such city, emergency personnel took more than minutes to arrive on of all calls involving life-threatening injuries last year. The city manager shares this information and encourages these first responders to 鈥渄o better.鈥� After months, the city manager selects an SRS of 400 calls involving life- threatening injuries and examines the response times. She then performs a test at the level of : versus , where is the true proportion of calls involving life-threatening injuries during this -month period for which emergency personnel took more than minutes to arrive.
a. Describe a Type I error and a Type II error in this setting.
b. Which type of error is more serious in this case? Justify your answer.
c. Based on your answer to part (b), do you agree with the manager鈥檚 choice of ? Why or why not?
Potato power problems Refer to Exercises and
a. Explain one disadvantage of using instead of when
performing the test.
b. Explain one disadvantage of taking a random sample of potatoes instead of potatoes from the shipment.
Don't argue Refer to Exercise 2. Yvonne finds that of the students say they rarely or never argue with friends. A significance test yields a -value of Interpret the -value.
A government report says that the average amount of money spent per U.S. household per week on food is about . A random sample of 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 . Is there convincing evidence that the mean weekly spending on food in this city differs from the national figure of ?
More lefties?In the population of people in the United States, about 10% are left-handed. After bumping elbows at lunch with several left-handed students, Simon wondered if more than of students at his school are left-handed. To investigate, he selected an SRS of students and found lefties .
To determine if these data provide convincing evidence that more than of the students at Simon鈥檚 school are left-handed, trials of a simulation were conducted. Each dot in the graph shows the proportion of students that are left-handed in a random sample of students, assuming that each student has a chance of being left handed.
a. State appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest.
b. Use the simulation results to estimate the P-value of the test in part (a). Interpret the -value.
c. What conclusion would you make?
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