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Information on determining the fairness of a die through an experiment, analyzing data from studies on hypnosis and migraines, and making predictions based on given data sets. Topics include hypothesis testing, linear regression, and probability.
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MAT/STA 325 Final Exam 10 Decemb er, 1997 Prof. Thistleton
(1) We will roll a 6 sided die to determine whether or not the die is fair. Supp ose we roll the die 600 times and obtain the following results:
Face 1 2 3 4 5 6 Numb er of Occurrences 88 95 112 108 101 96
At the = 0 : 01 level of signi cance, do you b elieve the die is fair?
(2) A study was published in 1978 ab out hypnosis and migraine headaches: C. Cedercreutz, Hypnotic Treatment of 100 cases of Migraine, in Hypnosis at Its Bicentennial. Data from this study are as follows:
Migraine Hypnosis Cured Better No Change Deep 13 5 0 Medium 10 26 17 Light 0 1 28
Based on this sample data, can you conclude that level of hypnosis and p erceived level of relief from migraine are indep endent at the = 0 : 05 level of signi cance?
(4) In a study to determine the e ects of air lters on the numb er of miles p er gallon obtained by a set of automobiles the following summary data were obtained:
Clean Filter Dirty Filter Sample Size 10 10 Sample Mean 25 22. Sample Standard Deviation 3.21 3.
Assume that these two samples come from normal p opulations with the same standard deviation. Test at the = 0 : 05 level of signi cance whether there is a di erence in numb er of miles p er gallon obtained with a dirty lter and with a clean lter.
(5) Supp ose that a normal p opulation has a mean height of = 50 cm and a standard deviation = 5 cm.
What is the probability that a randomly selected individual from this p opulation will have a height greater than 52 cm?
If you draw a sample of size n = 10 from this p opulation, what is the probability that your sample mean will exceed 52 cm?
If you draw a sample of size n = 50 from this p opulation, what is the probability that your sample mean will exceed 52 cm?
What is the probability of ipping a fair coin and obtaining more than 1080 heads on 2000 ips?
