A dietician investigated whether apples washed in hot water or in cold water tur

Question

A dietician investigated whether apples washed in hot water or in cold water turned
brown at different rates when exposed to air. She took 13 random apples and cut each in
half. She washed one half of each apple in hot water and the other half in cold water,
and then put both halves out in a tray. Her results (in hours until turning a particular
shade of brown) are in the table below. At = .01, did she see a difference between the
two treatments?
Hot Water Cold Water
Sample mean 5.50 4.85
Sample variance 2.60 2.00
A) No, because the test value –1.09 is inside the range (-3.055, 3.055).
B) No, because the test value –0.79 is inside the range (-3.055, 3.055).
C) Yes, because the test value –0.79 is inside the range (-3.012, 3.012).
D) Yes, because the test value –1.09 is outside the range (-3.012, 3.012).

Explanation / Answer

The test statistic is
t=(xbar1-xbar2)/[s1^2/n1 + S2^2/n2]

=(4.85-5.50)/sqrt(2.60/13+ 2.00/13)

=-1.09

The critical value is |t(0.005,n-1=12)|=3.05 (check student t table)

Answer: A) No, because the test value –1.09 is inside the range (-3.055, 3.055).

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