Question 133335: The engineer in a widget factory wants to test out a new form of raw materials. So a batch of widgets are made in the old manner as a control group and then a batch are made with the new materials as a comparison. If the widget weight is statistically the same on both sets, the new materials will be used. The weights of the 10 old process widgets and the 10 new process widgets are seen below.
Old New
36.19 36.20
35.80 36.62
36.00 36.03
36.19 36.40
36.18 36.44
36.11 36.02
36.13 36.12
36.48 36.56
35.98 36.05
36.40 36.44
1. Define this situation as either a 2 sample test or a paired test. Why?
2. Calculate a test statistic
3. Calculate a p-value
4. Give an accurate statement as to whether or not the new widget material should be used. Use a significance level of 0.05.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! ------------------------------------------
If the widget weight is statistically the same on both sets, the new materials will be used. The weights of the 10 old process widgets and the 10 new process widgets are seen below.
Old New
36.19 36.20
35.80 36.62
36.00 36.03
36.19 36.40
36.18 36.44
36.11 36.02
36.13 36.12
36.48 36.56
35.98 36.05
36.40 36.44
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1. Define this situation as either a 2 sample test or a paired test. Why?
2-sample test because the sets of data are independent.
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2. Calculate a test statistic
I used a TI calculator 2-Sample TTest to get
t = 0.4648
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3. Calculate a p-value
p-value = 0.3241
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4. Give an accurate statement as to whether or not the new widget material should be used. Use a significance level of 0.05.
New widget material should be used.
Ho was : mu1-mu2=0
Ha was : Mu1 is not m2
Since p-value is greater than 5%, fail to reject Ho; mean weights are
statistically the same.
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Cheers,
Stan H.
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