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# Hypothesis Test for the Mean: Dietitian Results

A dietitian 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 a= .01, did she see a difference between the two treatments?
Hot Water Cold Water Difference by apple

Sample mean 5.50 4.85 - 0.65
Sample standard deviation 1.612 1.414 - 0.198

a. Yes, because the test value -3.16 is outside the range (-3.055, 3.055).
b. No, because the test value -1.09 is inside the range (-3.055, 3.055).
c. Yes, because the test value -1.09 is inside the range (-3.01, 3.01).
d. No, because the test value -3.16 is outside the range (-3.01, 3.01).

#### Solution Preview

Step 1: Set the hypothesis.
H0 = Mean with hot water and cold water is same
H1 = Mean with hot water and cold water are different

Step 2:
Level of significance a=0.01

Step ...

#### Solution Summary

This post explains the step-by-step process for conducting five-step hypothesis testing for mean with two sample. The steps are explained with formulas and calculations along with interpretation of the final results.

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