An article includes the accompanying data on compression strength (lb) for a sam

Question

An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola.

Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. (Use

? = 0.05.)

State the relevant hypotheses. (Use ?1 for the strawberry drink and ?2 for the cola.)

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

State the conclusion in the problem context.

What assumptions are necessary for your analysis?

The distributions of compression strengths have equal variances.The distributions of compression strengths are the same.    The distributions of compression strengths are approximately normal.The distributions of compression strengths have equal means.

Beverage Sample   
Size Sample   
Mean Sample   
SD Strawberry Drink 10 536 23 Cola 10 558 17

Explanation / Answer

Null Hypothesis : H0: ?1 - ?2 <= 0

Alternate Hypothesis : Ha: ?1 - ?2 > 0

Test Statistics

t = [ (x1 - x2) - d ] / SE

t = -2.4325

p-value = 0.01317

Reject H0. The data suggests that cola has a higher average compression strength than the strawberry drink.

The distributions of compression strengths are approximately normal.

x1(bar) 536.00 x2(bar) 558.00 s1 23.00 s2 17.00 n1 10 n2 10 SE = sqrt[ (s12/n1) + (s22/n2) ] (s12/n1) 52.9000 (s22/n2) 28.9000 SE 9.0443 DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] } [ (s12 / n1)2 / (n1 - 1) ] 310.934 [ (s22 / n2)2 / (n2 - 1) ] 92.80 (s12/n1 + s22/n2)2 6691.24 DF = 17

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