At Kellogs Cereal Company the quality control manager claims that cartons filled

Question

At Kellogs Cereal Company the quality control manager claims that cartons filled by the newest machine have more cereal in them than cartons filled by the oldest machine. Samples taken from each machine, which operates independent of each other, yielding the following results:
Machine 1 Machine 2
sample size 25 36
sample mean 31.8oz 30.9oz
sample stdev 2.2oz 1.98oz

at the 0.05% level of significance, test the claim that the population mean for the newest machine (machine 1) is larger than the population mean for the oldest machine (machine 2)

Explanation / Answer

The test hypothesis is
Ho:1<=2
Ha:1>2

The test statistic is

Z=(xbar1 - xbar2)/[s1^2/n1 + S2^2/n2]

=(31.8-30.9)/sqrt(2.2^2/25 + 1.98^2/36)

=1.64

Given a=0.05, the critical value is Z(0.05)=1.645 (check standard normal table)

Since Z=1.64<1.645, we do not reject Ho.

SO we can not conclude that the claim that the population mean for the newest machine (machine 1) is larger than the population mean for the oldest machine (machine 2)

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