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Taste Test Example 4

Taste Test Example 4 - _Taste Test Example 4 for"cannot...

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__________________________________________Taste Test Example 4 for “cannot reject” p.1 To: Ms. Hardy From: Susie Example—9:30 a.m. Class Elementary Statistics Date: March 24, 2008 Re: Granola Bar Taste Test The results of whether KSU students preferred Publix or Quaker Oats granola bars are included in this email. The detailed analysis is in the appendix accompanying this document. The summary of the conclusions follows. I could not prove at 90% confidence that students preferred the Publix granola bar to the Quaker Oats granola bar. My sample proportion of 53% of the students preferring the Publix granola bar was too likely to happen by chance sample variation. In fact I had a 74% chance of observing this result just by chance. This P-value is higher than the 10% level of significance that I need to reject the null hypothesis of no preference. The conclusion that I could not say there was a preference for Publix granola bars was confirmed by the fact that the “no preference” proportion of 50% was one of the possible values for the 90% confidence interval. The confidence interval conveys that we can be 90% confident that the true proportion of students who prefer the Publix granola bars is between 39% and 66%. The margin of error for the confidence interval is 13.5%. If you desire a 3% margin of error, you would need to redo the experiment and increase the sample size from the existing 36 people to 729 people. Again, my detailed analysis follows. If you have any further questions, please contact me.
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__________________________________________Taste Test Example 4 for “cannot reject” p.2 Appendix Experimental Design I used the Completely Random Design for my experiment. I took 36 KSU students and randomly assigned them to the two treatment groups—either Publix first or Quaker Oats first. I made it so there were 18 people in each treatment group. (See Random Assignment to Treatments section below.) Quarter sections of both granola bars were placed on two 8-inch paper plates that looked alike, with the exception that each plate had the number one or two on it. Before the participants picked up their quarter sections from the plates, I instructed them not to express facially or vocally their preference for the granola bars, and not to talk to each other. I did not let the participants know which brands were being tested. After each person tried both granola bars, they wrote down which number they preferred on slips
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