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Chapter 9: Q .15. (page 564)
pg
No homework Refer to Exercises 1 and 9. What conclusion would you make at thelevel?
There is not enough convincing evidence to help the claim that less thanof the students at researcher's school finished their homework last night.
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How much juice? Refer to Exercise 3. The mean amount of liquid in the bottles is ml and the standard deviation is ml. A significance test yields a -value of . Interpret the -value.
Significance tests A test of against
based on a sample of size yields the standardized test statistic .
a. Find and interpret the -value.
b. What conclusion would you make at the significance level? Would
your conclusion change if you used instead? Explain your reasoning.
c. Determine the value of = the sample proportion of successes.
Battery life A tablet computer manufacturer claims that its batteries last an average of 10.5 hours when playing videos. The quality-control department randomly selects 20 tablets from each day鈥檚 production and tests the fully charged batteries by playing a video repeatedly until the battery dies. The quality control department will discard the batteries from that day鈥檚 production run if they find convincing evidence that the mean battery life is less than 10.5 hours. Here are a dot plot and summary statistics of the data from one day:
a. State appropriate hypotheses for the quality-control department to test. Be sure to define your parameter.
b. Check if the conditions for performing the test in part (a) are met.
Side effects A drug manufacturer claims that less than of patients who take its new drug for treating Alzheimer鈥檚 disease will experience nausea. To test this claim, researchers conduct an experiment. They give the new drug to a random sample of out of Alzheimer鈥檚 patients whose families have given informed consent for the patients to participate in the study. In all, of the subjects experience nausea.
a. Describe a Type I error and a Type II error in this setting, and give a possible
consequence of each.
b. Do these data provide convincing evidence for the drug manufacturer鈥檚 claim?
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: 鈥淵ou witness two students cheating on a quiz. Do you go to the professor?鈥� 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.
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