STATISTICS MATH 203
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This 2 page Class Notes was uploaded by Sadie Schroeder on Wednesday September 30, 2015. The Class Notes belongs to MATH 203 at Western Kentucky University taught by David Neal in Fall. Since its upload, it has received 16 views. For similar materials see /class/216741/math-203-western-kentucky-university in Applied Mathematics at Western Kentucky University.
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Date Created: 09/30/15
MATH 203 Sample Problems Solutions Among Independents reported preferences for the 2008 Democrat Presidential l nominee as of February 19 2007 were Hillary Clinton Barack Obama Al Gore John Edwards OtherUnd 3 00 25 10 5 25 However an April 2007 poll of 900 Independents gave the following preferences Hillary Clinton Barack Obama Al Gore John Edwards OtherUnd 288 261 108 54 189 a If the Feb 19 preferences still held in April then what would be the expected numbers of preferences for each candidate with a new poll of 900 Independents Hillary Clinton Barack Obama Al Gore John Edwards OtherUnd 900x035315 900x 025 225 900x01090 900x00545 900x 025 225 b To test the goodness of fit use your numerical values from Part a to find the Pearson test statistic 2 xZfz 6 8139 288 3152 I 261 2252 I108 902 I 54 452 I 189 2252 315 39 225 39 90 39 45 39 225 2 2 2 2 2 27 36 i 9 m19234 315 225 90 45 225 c Compute the Pevalue With 5 categories or bins use the rightetail of the x24 curve xzcdf19234 1E99 4 m 0000707 d Is there significant evidence now to reject the Feb preferences Use the P evalue to explain your conclusion in detail If the February preferences still held then there would be almost no chance only 00007 probability of getting the new poll of preference freuencies that differ so much from what would be expected We have strong evidence to now reject the preferences from February 2 Among the choices below what is your most important gadget My guesses for the responses are I Cell Phone I IPod I Laptop I Calculator I 45 30 20 5 But a survey of 400 students gives the following responses I Cell Phone I IPod I Laptop I Calculator I 200 115 70 15 a If my guesses were correct then what would be the expected numbers of responses for each choice in a survey of 400 students I Cell Phone I IPod I Laptop I Calculator I 400gtlt 045 180 400gtlt 030 120 400gtlt 020 80 400gtlt 005 20 b To test the goodness of fit use your numerical values from Part a to find the Pearson test statistic 2 x2fiei el 200 1802 I 115 1202 70 802 15 202 180 39 120 80 20 2 2 2 2 20 5 10 5 e493 180 120 80 20 c Compute the Pevalue With m 4 categories use the rightetail of the 38011 1 x2 3 curve xzcdf493 1E99 3e 0177 d Is there significant evidence to reject my guesses Use the P evalue to explain your conclusion in detail If my guesses were true then there would be about a 177 chance of getting response frequencies that differ as much from expected as these do We do not have strong enough evidence to reject the guesses
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