Question 136805: Need help having problems solving this problem
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
1. 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! 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 sample because the old and new data are independent samples. There is
no before/after involved. You simply have 10 widgets made with the old
and 10 widgets made with the new material.
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2. Calculate a test statistic
Find the mean weight of the old = 36.18375 and s=0.176549..
Find the mean weight of the new = 36.2575 and s=0.2087..
I ran a 2-Sample T-Test using Ho:u(old)-u(new)=0;Ha:u(old)-u(new) < 0
test statistic: t=-0.733103...
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3. Calculate a p-value
p-value = 0.238111
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1. Give an accurate statement as to whether or not the new widget material should be used. Use a significance level of 0.05.
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Since the p-value is greater than 5%, Fail to reject Ho.
The new material may be used.
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Cheers,
Stan H.
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