Question 235409: I need your help in working this problem out. Thank you very much...
A watch manufacturer creates watch springs whose properties must be consistent. In particular, the standard deviation in their weights must be no greater than 2.0 grams. Fifteen watch springs are selected from the production line and measured; their weights are 1, 4, 8, 7, 1, 5, 1, 4, 1, 4, 3, 9, 1, 3, and 2 grams. Assume = 0.01.
· State the null and alternate hypotheses
· Calculate the sample standard deviation
· Determine which test statistic is appropriate (chi-square or F), and calculate its value.
· Determine the critical value(s).
· State your decision: Should the null hypothesis be rejected?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A watch manufacturer creates watch springs whose properties must be consistent. In particular, the standard deviation in their weights must be no greater than 2.0 grams. Fifteen watch springs are selected from the production line and measured; their weights are 1, 4, 8, 7, 1, 5, 1, 4, 1, 4, 3, 9, 1, 3, and 2 grams. Assume = 0.01.
· State the null and alternate hypotheses
Ho: sigma^2 <= 4 (claim)
Ha: sigma^2 > 4
· Calculate the sample standard deviation
std of the sample = 2.667
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· Determine which test statistic is appropriate (chi-square or F), and calculate its value.
Chi-Sq = (n-1)*s^2/sigma^2 = 14*2.667^2/4 = 24.895
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· Determine the critical value(s)
Chi-Sq lower = 4.075 ; Chi-Sq upper = 31.32
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State your decision: Should the null hypothesis be rejected?
Since the ts is not in either rejection interval, do not
reject Ho based on these test results.
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Cheers,
Stan H.
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