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On each die in a set ·of six dice the pips on each face are diamonds. It is suggested that the weight of the stones will cause the ·"five" or "six" faces to fall downward, and hence the "one" and "two " faces to fall upward, more frequently than they would with fair dice . To test this conjecture, a trial is conducted as follows: The throwing of a one or two is called a success. The six dice are thrown together 64 times and the frequencies of throws with 0, 1, 2, 6 . . . successes summed over all six pairs are as follows:
(a) What would be the theoretical probability of success and the mean and variance of the above frequency distribution if all the dice were fair?
(b) What is the empirical probability of success calculated from the data and what is the sample average and variance?
(c) Test the hypothesis that the mean and variance have their theoretical values.
(d) Calculate the expected frequencies in the seven "cells" of the table on the assumption that the probability of a success is exactly 1/3.
(e) Can you think of a better design for this trial?
Let X1, ... , Xn be i.i.d. r.v.'s with (?nite) unknown mean m and (?nite) known variance s 2, and suppose that n is large. i) Use the CLT to construct a con?dence interval for m with approximate con?dence coef?cient 1 - a;
type your question here the five summery for production order size in thousends pounds for steel tubing is min16.5 q132
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In 1990, 5.8% of job applicants who were tested for drugs failed the test. At the 0.01 significance level, test the claim that the failure rate is now lower if a simple random sample of 1520 current job applicants results in 58 failures. Does the ..
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