Critical Value Method – Examples

You have learnt how to perform the three steps of the critical value method with the help of the AC sales problem as well as the above product lifecycle comprehension problem, which was a two-tailed test. But what would happen if it were a one-tailed test? Let’s watch the video below to understand.

Attempt the following questions to complete this one-tailed test.

You can download the z-table from the attachment below. It will be useful in the subsequent questions.


Government regulatory bodies have specified that the maximum permissible amount of lead in any food product is 2.5 parts per million or 2.5 ppm. Let’s say you are an analyst working at the food regulatory body of India FSSAI. Suppose you take 100 random samples of Sunshine from the market and have them tested for the amount of lead. The mean lead content turns out to be 2.6 ppm with a standard deviation of 0.6.

One thing you can notice here is that the standard deviation of the sample is given as 0.6, instead of the population’s standard deviation. In such a case, you can approximate the population’s standard deviation to the sample’s standard deviation, which is 0.6 in this case.

Answer the following questions in order to find out if a regulatory alarm should be raised against Sunshine or not, at 3% significance level.

You can look at the solution of this comprehension from this video .

Note: At 2:06, the sample size would be n instead of m while calculating critical value)

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