A bottling company is known to fill wine bottles with amounts that follow a Norm

Question

A bottling company is known to fill wine bottles with amounts that follow a Normal distribution. As a quality control officer, you are concerned that the amount of wine in each bottle might be different from the 750 mil indicated on the label. Hence, you decide to test the hypothesis, at a alpha = 0.05, that the amount of wine in each bottle is, on average, different from 750 mil. You collect a sample of 35 bottles and find that x bar = 755 mil and S = 5 mil. Describe, step by step, your hypothesis testing procedure.

Explanation / Answer

Let X follows normal distribution. Where

Population mean = 750

Standard deviation is not know

Sample size=35

We used t-test to test the hypothesis

Null hypothesis: the population mean=750

Vs

Alternative hypothesis: the population mean is not equal to 750

Test procedure

t = sqrt(n)* (Xbar - mu)/S

= sqrt(35)*(755-750)/5

=5.91

Therefore t-cal=5.91

t-val(34,0.05)=1.96

As tcal > tval we reject the null hypothesis with 5% level of significance.

So the amount of beer in every bottle on average is different than 750ml.

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