Question 269148: I don't quite understand this and need help, please.
A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. The weights (in ounces) of the cereal in a random sample of 8 of its cereal packets are listed below.
14.6 13.8 14.1 13.7 14.0 14.4 13.6 14.2
At the 0.01 significance level, does the sample support the company’s claim that the mean weight is at least 14 ounces? You may assume the weight of cereal packets is normally distributed.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. The weights (in ounces) of the cereal in a random sample of 8 of its cereal packets are listed below.
14.6 13.8 14.1 13.7 14.0 14.4 13.6 14.2
mean of the sample:14.05
std of the sample: 0.3464
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At the 0.01 significance level, does the sample support the company’s claim that the mean weight is at least 14 ounces? You may assume the weight of cereal packets is normally distributed.
Ho: u >= 14 (Co. claim)
H1: u < 14
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Critical value for right-tail test with alpha = 1% and df = 7 :
invT(0.01,7) = 2.9980
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Test statistic: t(14.05) = (14.05-14)/[0.2464/sqrt(8)] = 0.5740
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Conclusion: Since the ts is less than the cv, fail to reject Ho.
The test results support the company's claim.
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Cheers,
Stan H.
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