__________________________________________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 Pvalue 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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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 8inch 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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 Spring '08
 Hardy
 Statistics, Statistical hypothesis testing, granola bars, Publix

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