SOLUTION: A manufacturer claims that the mean weight of flour in it�s bags is 32.1 ounces. A advocacy group gathers a sample of 12 bags of flour from the manufacturer. The weight are is the

Question 1104963: A manufacturer claims that the mean weight of flour in it�s bags is 32.1 ounces. A advocacy group gathers a sample of 12 bags of flour from the manufacturer. The weight are is the table below: 31.6 31.0 32.1 32.2 32.5 31.9 31.9 31.6 31.7 32.1 31.3 31.8 Assume that a preliminary work has shown that the data comes from a normally distributed variable. Can the advocacy group claim that the average weight of flour in the bags is less than 32.1 ounces at the 0.025 significance level? You use rejection regions to support your argument. Be sure to state the Null and Alternative hypothesis, the test statistic, and decide whether to reject or not reject the null hypothesis. Include a sketch of distribution you used with the corresponding shaded areas. In the end, you must interpret the decision in the context of the original claim.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A manufacturer claims that the mean weight of flour in it�s bags is 32.1 ounces. A advocacy group gathers a sample of 12 bags of flour from the manufacturer.
The weight are is the table below: 31.6 31.0 32.1 32.2 32.5 31.9 31.9 31.6 31.7 32.1 31.3 31.8
Sample mean = 31.8
Sample std = 0.41
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Assume that a preliminary work has shown that the data comes from a normally distributed variable. Can the advocacy group claim that the average weight of flour in the bags is less than 32.1 ounces at the 0.025 significance level? You use rejection regions to support your argument. Be sure to state the Null and Alternative hypothesis, the test statistic, and decide whether to reject or not reject the null hypothesis. Include a sketch of distribution you used with the corresponding shaded areas. In the end, you must interpret the decision in the context of the original claim.
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Ho: u >= 32.1
Ha: u < 32.1 (claim)
Test statistic:: t(31.8) = (31.8-32.1)/0.41 = -0.7317
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Rejection region:: Find the t-value with a left tail of 0.025 when df = 11
invT(0.025,11) = -2.201
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Rule:: Reject Ho if t < -2.201
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Conclusion:: Since the test statistic is not < -2.201, fail reject Ho.
Conclusion:: The test results do not support the claim that u<32.1.
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Cheers,
Stan H.
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