At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a

Question

At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 540 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml. A sample of 36 bottles shows a mean fill of 538 ml. At the.05 significance level, can we conclude that the mean fill of the bottles are different from 540 ml? a. Write the hypothesis statements. b. Explain what test statistic will be used and why. c. Compute the test statistic. d. State the decision rule and sketch it. Based on the decision rule, do you accept or reject the Null Hypothesis? e. State your findings.

Explanation / Answer

Set Up Hypothesis
Null Hypothesis H0: U=540
Alternate Hypothesis H1: U!=540
Test Statistic
Population Mean(U)=540
Given That X(Mean)=538
Standard Deviation(S.D)=4
Number (n)=36
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=538-540/(4/Sqrt(36)
Zo =-3
| Zo | =3
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =3 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != -3 ) = 0.0027
Hence Value of P0.05 > 0.0027, Here we Reject Ho

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