Question

The Crown Bottling Company has installed a new bottling process that will fill 12-ounce bottles of Cola. Both overfilling and underfilling of bottles is undesirable. The company wishes to see whether the mean bottle fill, µ, is close to the target of 12 ounces. The company samples 43 bottles. The sample mean is 11.89 and the standard deviation is such that s=0.11. a) Use a hypothesis test, at a 1% level of significance to determine whether the filler should be adjusted. (4 points) b) Now suppose the company is worried about underfilling. Use a one-tailed hypothesis test at a 1% significance level to determine whether the mean is less than 11.95 ounces.

Answer 1

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n = 43

xbar = 11.89

mu = 12

s = .11

a)

Mu = 12

Mu != 12

test-statistics = (xbar - Mu)/(s/sqrt(N)) = (11.89-12)/(11/sqrt(43)) = -0.066

p-value= .95, >> alpha of 0.01

We can't reject Ho due to lack of evidence and sayt that the filler NEED NOT BE should be adjusted.

b)

P(x<11.95 )= P(t < (11.95-12)/(11/sqrt(43)) = P(t< - .03) = .97, >> .01.

We fail to reject Ho and conclude that : Mean is not less than 11.95 ounces