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Unformatted text preview: ____________ _Taste Test Example for “reject Ho with a very low P-value compared to α ” p.1 To: Ms. Hardy From: Bonnie Berezo—11:00 a.m. Elementary Statistics Date: March 22, 2008 Re: Cheese Cracker Taste Test The results of the Cheez-it/Cheese Nip cracker taste test for people who attended the Winter Blast Horse Show are included in this email. The detailed analysis is in the appendix accompanying this document. The summary of the conclusions follows. You desired to determine whether you should invest in Cheez-it or Cheese Nip stock based on Winter Blast Horse Show attendee opinions. The hypothesis test showed a significant preference for Cheez-it crackers with a P-value of .0076608502, which is considerably below the significance level of .10. Thus, I had less than a 1% chance of obtaining my sample result of 72% of the attendees preferring Cheez-it crackers, if there were no preference between the two crackers. The rarity of the sample result under the “no preference” assumption, combined with the fact that we did observe the sample proportion of 72%, prompts us to conclude that our assumption of “no preference” is incorrect. We are 90% confident that there is a preference for Cheez-it crackers. This conclusion was confirmed by the fact the 90% confidence interval did not contain the “no preference” proportion of 50%. We are 90% confidence that the true proportion of Winter Blast Horse Show attendees who preferred Cheez-it crackers is between 60% and 85%. As a result, I would suggest that you buy stock in Cheez-it rather than Cheese Nip. If you want to have a more accurate estimate of the true preference for Cheez-it crackers, I would suggest that we increase the sample size and redo the taste test. By increasing the sample size from the existing 36 people to 576 people, we would reduce the current margin of error of 12.5% to 3%, giving us a total confidence interval width of 6%. Again, my detailed analysis follows. If you have any further questions, please contact me. ____________ _Taste Test Example for “reject Ho with a very low P-value compared to α ” p.2 Appendix Experimental Design I used the Completely Random Design for my experiment. I took 36 Winter Blast attendees and randomly assigned them to the two treatment groups—either Cheez-it first or Cheese Nip first. I made it so there were 18 people in each treatment group. (See Random Assignment tomade it so there were 18 people in each treatment group....
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This note was uploaded on 04/18/2008 for the course MATH 1107 taught by Professor Hardy during the Spring '08 term at Kennesaw.
- Spring '08