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Show that for k = 2 the likelihood ratio statistic of Exercise 25 can be expressed in terms of the ratio of the two sample variances and that the likelihood ratio test can, therefore, be based on the F distribution.
Exercise 25
Independent random samples of sizes n1, n2, ... , and nk from k normal populations with unknown means and variances are to be used to test the null hypothesis = =···= against the alternative that these variances are not all equal.
(a) Show that under the null hypothesis the maximum likelihood estimates of the means μ1 and the variances are
(b) Using the results of part (a), show that the likelihood ratio statistic can be written as
Find the probability that the mean GPA of a random sample of 20 students selected from this university is 2.95 or lower.
Poisson distribution with a mean of 8.8 tickets per day. Find the probability that less than six tickets are written in one hour given that the police works for 12 hours.
Provide an example of how an ANOVA could expand on the results of a t-test. In other words, think of an example (related to the field of psychology) in which you could use a t-test, and then note how the comparison could change if an ANOVA was use..
using two independent samples we test for a hypothesized difference between two population means. the population
A company produces two products, A and B, which have profits of $9 and $7, respectively. Formulate a linear programming model to determine the optimal product mix that will maximize profit. What are the sensitivity ranges for the objective function c..
a recent survey reported that in a sample of 300 students who attend two-year colleges 105 work at least 20 hours per
Find the probability that in a given year a) exactly one major hurricane will strike the U.S. mainland, b) at most one major hurricane will strike the U.S. mainland.
Determine the standard score for the value x=452 realative to its sample, where the sample mean is 500 and the standard deviation is 32.
How does your answer change if you flip the coin 400 times in- stead?
In order that the sample proportion and the population proportion not differ by more than 0.05 with 95% level of confidence, what sample size should be used?
The following data represents the running time of films produced by 2 motion picture companies. Assume these are independent samples
The table below lists deaths in Georgia in 2004, the estimated population of Georgia in 1994 and the U.S. population according to the 2000 census. Calculations should be done by hand, but feel free to use software to check your work.
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