The crown Bottling Company has just installed a new bottling

The crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable. In order to verify that the filler is set up correctly, the company wishes to see whether that mean bottle fill, mu, is close to the target fill of 16 ounces. To this end, a random sample of 36 filled bottles is selected from the output of a test filler run with mean 16.03. Let significance level be 0.02. Assume population standard deviation is 1. If the sample results cast a substantial amount of doubt on thehypothesis that the mean bottle fill is the desired 16 ounces, then the filler

Solution

Null Hyp: mean bottle fill, mu is 16 ounces

H0: mu = 16

Alt Hyp: mean bottle fill, mu isnot equal to 16 ounces

Ha: mu not equal to 16

It is a two tailed test

sample of 36 filled bottles; mean xbar = 16.03; stdev = 1

Since population stdev is given we use z test

Test Stat z = (xbar - mu)/std error = (16.03 - 16)/1/sqrt(36) = 0.18

p value = 0.8572

Ans) d. 0.8572

alpha = 0.02

At alpha 0.02 critical value = +2.33

Rejection regions are if Z<-2.33 or Z>2.33, we reject the null hypothesis.

Answer: (-?, -2.33] [2.33, ?)

Since test stat does not lie in the rejection region we fail to reject the Null hypothesis

type two error is possible