Date: 05/11/98 at 05:38:58 From: Danilou Subject: Statistics and Research Methods I was wondering if you could help me with hypothesis testing. I don't really understand how you find H0 and H1. I understand that the null hypothesis is the same as your sample proportion or population. So in the instance of the stemplot with p = 0.7, then H0 is p = 0.7. Here is my stemplot: Stems:0.1's Leaves:.01's +| 9| 9|33 9|0 8| 8|66 8| 8|33333333333 8|000000000000000 7| 7|6666666666666666666666666 7| 7|3333333333333333333 7|00000000000000000000000000000000000 6| 6|6666666666666666666666666666666666666666666 6| 6|333333333333333 6|000000000000000 5| 5|666666666 5| 5|333333 5|0000 4| -| The stemplot is showing the distribution of the sample proportion P when two hundred samples of size 30 are drawn from a population with proportion p = 0.7. I have worked out that H0 is p = 0.7 and H1 is p => 0.7. The significance level is 0.05. I do not understand the test statistic or its value. I also do not know the P-value, or what I am supposed to write for a conclusion. This computer-generated sampling distribution is supposed to test, at the 5% level of significance, the hypothesis that more than 70% of students have access to a computer at home. Thanks, Danilou
Date: 05/11/98 at 09:10:28 From: Doctor Statman Subject: Re: Statistics and Research Methods Dear Danilou, If I understand the question, then the stemplot that you have included represents what happened when you took a bunch of samples from a population that is known to have a p = 0.7. Even though you and I know that p = 0.7, the sample proportion for each sample does not usually come out to be 0.7. If you flip a coin ten times, you don't always get five heads, right? Same here. Even though p = 0.7, you don't always get 70% exactly. The stemplot shows one collection of results sampled from your population where p = 0.7. If I repeated the experiment, I would get a stemplot that would probably look a lot like yours, but it wouldn't be exactly the same. Both of our stemplots would be the results of simulations. If I repeated the experiment a bazillion times -- many more than would be practical -- I would see a regular pattern emerge. The sampling distribution would always be bell-shaped with a center at 0.7. So the stemplot represents the sampling distribution from one experiment, and it looks roughly bell-shaped. But there is a smooth curve, living "behind the scenes," that represents what would happen if you could repeat the experiment forever: you would get a perfect bell-shaped curve, which represents the theoretical sampling distribution. Hope this helps! Statistically yours, -Doctor Statman, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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