Test the given claim about the means of two populations. Be sure to state any re

Question

Test the given claim about the means of two populations. Be sure to state any requirements for the test, the null and alternative hypothesis, the test statistic and pvalue as well as a valid conclusion. Assume that two dependent samples have been randomly selected from normally distributed populations.

The table below shows the weights of seven subjects before and after following a particular diet for two months.

Before: 179, 191, 152, 198, 170, 170, 164
After : 172, 182, 150, 203, 156, 172, 152

Using a 0.01 level of significance, test the claim that the diet is effective in reducing weight.

Explanation / Answer

Okay, what you have here is a sample of 7 people with a before and after treatment. What you want to use in this situation is a "matched pairs" or "dependent" t test (those mean the same thing, just called different in different books) the first thing you are going to do is make a new variable called differences. Differences = Before - After. Find the mean and standard deviation of this new variable (sample standard deviation of course) and find the average = 4.43, std dev = 8.77 Null Hypthesis: the diet didn't affect a change; in other words, the before - after variable is 0. (in math, mu = 0) Alternative Hypthesis: the diet did affect a change; in other words, the pre-diet weight (before) is more than the post-diet weight, sp this is greater than 0) (in math, mu > 0) now calculate the test statistic: t = (d_bar - 0)/(s/sqrt(n)) (4.43 - 0)/(8.77/sqrt(7)) = 4.43/3.32 = 1.34 dont forget 7 - 1 degrees of freedom. look up the cut-off value _cut-off = 3.143 (note I used http://www.stat.tamu.edu/~west/applets/tdemo.html to get my value - this may be a little different from the table in your book) Since test statistic

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