1. You have been asked to check if the weight of the bottles filled by Abe is gr

Question

1. You have been asked to check if the weight of the bottles filled by Abe is greater than the weight of the bottles filled by Becky. You select a sample of 12 bottles filled by Abe and find that the average weight of the bottles is 8.35 ounces with a standard deviation of 1.27 ounces. You then select a sample of 14 bottles filled by Becky and find that the average weight of the bottles is 7.85 ounces with a standard deviation of 1.41 ounces. At the 0.05 level of significance, is the mean weight of the bottles filled by Abe's machine greater than the mean weight of the bottles filled by Becky's machine?

Explanation / Answer

Hypothesis:
H0 : mu1 = mu2
Ha : mu1 > mu2

Test statistics:

x1 = 8.35 , s1 = 1.27 , n1 = 12 , x2 = 7.85 , s2 = 1.41, n2 = 14

t = (x1 -x2)/sqrt(s1^2/n1 +s2^2/n2)
= ( 8.35 - 7.85)/sqrt(1.27^2/12 + 1.41^2/14)
= 0.9510

P value is calculated using t = 0.9510
with df = 24 at 0.05 significance level

P value = .1755

we cannot reject the null hypothesis.

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