SOLUTION: A consumer advocacy group suspects that a local supermarket's 500 grams of sugar actually weigh less than 500 grams. The group took a random sample of 20 such packages, weighed eac

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Question 899413: A consumer advocacy group suspects that a local supermarket's 500 grams of sugar actually weigh less than 500 grams. The group took a random sample of 20 such packages, weighed each one and found the mean weight for the sample to be 496 grams with a standard deviation of 8 grams. Using 10% significance level, would you conclude that the mean weight is less than 500 grams? Also, find the 90% confidence interval of the true mean.
what is the hypothesis?
H0:
H1:
The level of significance is a= ___, df= ___, and the critical region for the value of one sample t-test
decision rule:
conclusion:
compute for the confidence interval:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

Ho: u ≥ 500

Ha: u < 500

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t(496) = (496-500)/[8/sqrt(20)] = 4/1.7889 = 2.236

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p-value = P(t> 2.236 when df = 19) = tcdf(2.236,100,19) = .9825

As .9825 > .10,  No, would not conclude mean is <500 

ME = 1.645(8/sqrt(25))

CI: = 496 - ME < mu < 496 + ME