Statistics and Probability Answers

survey of 31 randomly selected students finds that they save a mean of $82 per semester by

using a website. Assume the date comes from a normal distribution and the sample standard deviation is $18 per month.

Confidence Interval: What is the 99% confidence interval to estimate the population mean? (Round your

answers to two decimal places.)

____< u < _____

A sample of 25 women had a variance in IQ scores of 62. A sample of 18 men had a variance of 72. Do the women have a smaller variance in IQ scores at the 0.01 level of significance? Assume both populations are normally distributed

A researcher claims that 10 year olds watch 6.6 hours of TV daily with SD = 2.5 hours. You try to verify this with the following sample data of 100 and a sample mean of 6.1 hours. Test the claim of the researcher. Test at α = .01

A Research Director of a certain university wants to replicate the result of the study 10 years ago with a standard deviation of 0.14. He wants to estimate the population mean to within an error of 0.04 of its true value. Using 95% confidence level, what is the sample size that he needs?

The joint probability density of X, Y is

f(x, y) = e ^{−(x + y)} xi > 0 i = 1, 2

0 otherwise

Using the change of variable technique, determine the joint distribution of Z = X and W = X + Y

Suppose that X1 and X2 have the joint probability distribution

f(x1, x2) = kx1x2 x1 = 1, 2, 3 x2 = 2, 3, 4

0, otherwise

Find the value of k so that the two variables are independent of each other

Let X, Y be independent and identically distributed random variables, each having Poisson distribution with rate parameter λ. Find the probability generating function of W = X + Y and hence the mean and variance of W