# 1. Consider two independent random variables X and Y. Random variab...

## Question

1. Consider two independent random variables X and Y. Random variable X has a x^2 distribution with v(sub)x=25 degrees of freedom and random variable Y has a x^2 distribution of v(sub)y=29 degrees of freedom. Consider the random variable W= X/Y. W has a distribution which you can easily derive. Find the 95th percentile of the distribution W.

2.         Group 1    Group 2    Group 3   Group 4
Mean    81.98       112.28    112.08    73.63
SD         8.51          7.50          7.11       5.17
n          21.00       21.00       21.00      21.00

(SD) = standard deviation (n) = sample size

The above data is for 4 independent groups. You construct a 90% confidence interval on the quantity: k = mu(sub)1 - mu(sub)2 - mu(sub)3 + mu(sub)4
What are the endpoints of the interval?

3. Using the above data from the previous question, compute the t- statistic for testing the null hypothesis: H(sub)0 : mu(sub)1 - mu(sub)2 - mu(sub)3 + mu(sub)4 = 0

(H(sub)0 = null hypothesis)

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