A beverage company has a machine that is supposed to fill soda bottles with two

Question

A beverage company has a machine that is supposed to fill soda bottles with two liters of soda. To check that the machine is operating correctly, not over or under filling, a sample of 81 bottles was selected and the contents of each bottle was determined. The sample mean is 1.93 liters of soda. Does this indicate that the machine is improperly filling the bottles? Use a mean = 2.0 liters, a standard error = .02 liters and alpha = 1%. a) What is the null hypothesis? b) What is the alternative hypothesis? c) What is the critical value (s)? d) What is the decision rule? e) Draw a labeled diagram including acceptance and rejection areas, the mean, the standard error, the shaded significance region, and the test statistic. f) What is your conclusion?

Explanation / Answer

Below are the null and alternate hypothesis
H0: mu = 2
H1: mu not equals to 2

For alpha = 1%, z-critical value = +/- 2.58 (as this is two tailed test we need to consider alpha/2 while finding the z critical value from the standard z table)

If the calculated value of z-statistics fall beyond the critical value of z, we reject the null hypothesis.

Here, test statistics
z = (1.93 - 2)/0.02 = -3.5

As test statistics is less than -2.58 (critical value), we reject the null hypothesis

This means, there is evidence that the is improperly filling the bottles.

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