1 .) The manufacturer of KELLOGGS Corn Flakes wants to determine whether the cer

Question

1.)  The manufacturer of KELLOGGS Corn Flakes wants to determine whether the cereal-filling process is working properly. Throughout the entire packaging process, the population mean (u) of 368 grams per box remains to be the same and no corrective action is needed. To evaluate the 368-gram requirement, the researcher selects a random sample of 25 cereal boxes and indicates a sample mean (x) of 372.5 grams and the population standard deviation is 15 grams. At the 0.05 level of significance, compare the results. What conclusions do you reach? (Use the five-step method of t statistic formula)

Explanation / Answer

Set Up Hypothesis
Null,mean remains to be the same H0: U=368
Alternate, H1: U!=368
Test Statistic
Population Mean(U)=368
Sample X(Mean)=372.5
Standard Deviation(S.D)=15
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =372.5-368/(15/Sqrt(25))
to =1.5
| to | =1.5
Critical Value
The Value of |t | with n-1 = 24 d.f is 2.064
We got |to| =1.5 & | t | =2.064
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != 1.5 ) = 0.1467
Hence Value of P0.05 < 0.1467,Here We Do not Reject Ho

We have evidence that mean remains to be the same

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