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Chapter 9: Q.2.1 (page 539)
Describe a Type I error in this setting.
Type I error occurs if the null hypothesis is dismissed regardless of whether it is right.
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鈥淚 can鈥檛 get through my day without coffee鈥� is a common statement from many students. Assumed benefits include keeping students awake during lectures and making them more alert for exams and tests. Students in a statistics class designed an experiment to measure memory retention with and without drinking a cup of coffee one hour before a test. This experiment took place on two different days in the same week (Monday and Wednesday). Ten students were used. Each student received no coffee or one cup of coffee, one hour before the test on a particular day. The test consisted of a series of words flashed on a screen, after which the student had to write down as many of the words as possible. On the other day, each student received a different amount of coffee (none or one cup). (a) One of the researchers suggested that all the subjects in the experiment drink no coffee before Monday鈥檚 test and one cup of coffee before Wednesday鈥檚 test. Explain to the researcher why this is a bad idea and suggest a better method of deciding when each subject receives the two treatments.
(b) The data from the experiment are provided in the table below. Set up and carry out an appropriate test to determine whether there is convincing evidence that drinking coffee improves memory.
To determine the reliability of experts who interpret lie detector tests in criminal investigations, a random sample of such cases was studied. The results were
(a) .
(b) .
(c) .
(d) .
(e) .
You are testing against based on an SRS of observations from a Normal population. What values of the statistic are statistically significant at thelevel?
(a)
(b)
(c)
(d)
(c)
Packaging CDs (6.2, 5.3) A manufacturer of compact discs (CDs) wants to be sure that their CDs will fit inside the plastic cases they have bought for packaging. Both the CDs and the cases are circular. According to the supplier, the plastic cases vary Normally with mean diameter and a standard deviation . The CD manufacturer decides to produce CDs with mean diameter . Their diameters follow a Normal distribution with .
(a) Let X = the diameter of a randomly selected CD and Y = the diameter of a randomly selected case. Describe the shape, center, and spread of the distribution of the random variable X = Y. What is the importance of this random variable to the CD manufacturer?
(b) Compute the probability that a randomly selected CD will fit inside a randomly selected case.
(c) The production process actually runs in batches of 100 CDs. If each of these CDs is paired with a randomly chosen plastic case, find the probability that all the CDs fit in their cases.
Does this paper give convincing evidence that the mean amount of sugar in the hindguts under these conditions is not equal to ? Justify your answer.
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