Null Hypothesis, Deviation
Date: 08/09/97 at 18:57:35 From: Heather Subject: Statistics A statistician believes that on the average the members of a group of people weigh 120 pounds. To test this belief, the statistician weighs 7 people with the following results: 121, 125, 118, 130, 117, 123, 120 a. What is the statistician's null hypothesis? b. What is the alternative hypothesis? c. What mean and standard deviation would you estimate from the given data? d. What conclusion would you draw about the statistician's belief at the 5 percent significance level? Thanks.
Date: 08/09/97 at 19:54:27 From: Doctor Anthony Subject: Re: Statistics >a. What is the statistician's null hypothesis? That the average is 120 pounds. >b. What is the alternative hypothesis? That the average differs from 120 - either higher or lower. >c. What mean and standard deviation would you estimate from the given data? Mean of sample is 854/7 = 122 sample variance = 104308/7 - 122^2 = 17.143 s.d = 4.1404 Best estimate of population variance = (7/6)(17.143) = 20.00 " " " s.d = 4.472 The s.d. of the sampling distribution is 4.472/sqrt(7) = 1.690 (also known as standard error of the mean) >d. What conclusion would you draw about the statistician's belief at the 5 percent significance level? 122 - 120 We compute z from z = --------- = 1.1832 1.69 We compare this value against a z value of 1.96, which is the two-tailed significance threshold for the 5-percent level (2.5 percent in each tail). Since 1.18 < 1.96 our result is not significant, and we do not reject the null hypothesis that the mean is 120 pounds. This does not mean that it is 120, but a sample, size 7, from a population with mean 120 has a better than 5 percent probability of giving a mean as high as 122. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.