Please be as in-depth as possible with the solution. Thanks.

62. In a genetics experiment, investigators examined 300 chromosomes of a particular type nd counted the number of sister-chromatid exchanges on each one ("On the Nature of Sister-Chromatid Exchanges in 5-Bromodeoxyuridine-Substituted Chromosomes," Genetics, 1979: 1251-1264). A Poisson model was hypothesized for the distribution of the number of exchanges. Test the fit of such a model to the accompanying data by first estimating and then combining the

frequencies for x 5 8 and x 5 9. x: 0 1 2 3 4 5 6 7 8 9 Frequency: 6 24 42 59 62 44 41 14 6 2

66. The Charpy V-notch impact test is to be applied to a sample of 20 specimens of a certain alloy to determine transverse lateral expansion at 110F. To be suitable for a particular application, true average expansion should be less than 75 mils. The alloy will not be used unless there is strong evidence that the criterion has been met. Assuming a normal distribution and a test with 5 .01, what is the probability that a type II error will be committed and the alloy not used when in fact 5 72 and 5 5? What is this probability when 5 70 and 5 5?

76a

76. When the population distribution is normal, it can be shown that the variable X 2 5 (n 2 1)s 2 y 2 has a chi- squared distribution with n 2 1 df. This can be used as a basis for testing H0 : 5 0 , as follows:

Replace 2 in X 2 by its hypothesized value 2 0 to obtain a test statistic. If the alternative hypothesis is Ha : . 0 , the P-value is the area under the n 2 1 df chi-squared curve to the right of the calculated X 2 (an upper-tailed test).

a. To ensure reasonably uniform characteristics for a particular application, it is desired that the true standard deviation of the softening point of a certain type of petroleum pitch be at most .50C. The softening points of ten different specimens were determined, yielding a sample standard deviation of .58C. Assume that the distribution from which the observations were selected is normal. Does the data contradict the uniformity specification? State and test the appropriate hypotheses using 5 .01.