Question 150654: A manufacturer wants to increase the absorption capacity of a sponge. Based on past data, the average sponge could absorb 3.5 ounces. After the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9. What is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A manufacturer wants to increase the absorption capacity of a sponge.
Based on past data, the average sponge could absorb 3.5 ounces.
After the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9.
What is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge?
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Ho: u = 3.5
Ha: u > 3.5
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x-bar of the data = 3.76
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Comment: The decision rule depends on whether you use a "t" or
a "z" critical value.
If "t" the decision rule is "reject Ho if t is above 2.821".
If "z" the decision rule is "reject Ho if z is above 2.326".
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Cheers,
Stan H.
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