# Hypothesis testing

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A half-liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml.

(a) Which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why?

(b) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance.

(c) If a sample of 16 bottles shows a mean fill of 515 ml, does this contradict the hypothesis that the true mean is 520 ml?

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##### Solution Summary

A hypothesis is tested using a 2-tailed decision rule.

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A half-liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml.

(a) Which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why?

We will use Normal distribution (z table) as the filling process follows a normal distribution with a known process standard deviation.

Please refer to table below for the criteria

When the Population standard deviation is known When the Population standard deviation is not known

Sample size is larger than 30 Normal distribution, z table Normal distribution, z table

Sample size is 30 or less and we assume that the population is ...

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