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A local fast food company sells a 16-oz soft drink. To determine if the soft drinks served contain less than the advertised 16 oz, a random sample of 20 drinks is chosen and the amount of drink in each cup is measured (without ice). The mean amount of soft drink was found to be 15.5 oz with a standard deviation of 0.4 oz. Based on the sample results we cannot claim that the soft drink contains less than 16 oz. Which form of statistical inference does this conclusion represent?

Question

A local fast food company sells a 16-oz soft drink. To determine if the soft drinks served contain less than the advertised 16 oz, a random sample of 20 drinks is chosen and the amount of drink in each cup is measured (without ice). The mean amount of soft drink was found to be 15.5 oz with a standard deviation of 0.4 oz. Based on the sample results we cannot claim that the soft drink contains less than 16 oz. Which form of statistical inference does this conclusion represent?

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Solution

The conclusion represents a form of statistical inference known as hypothesis testing. In this case, the null hypothesis would be that the mean amount of soft drink is equal to 16 oz. The alternative hypothesis would be that the mean amount of soft drink is less than 16 oz. The sample data was used to test these hypotheses. Since the mean of the sample was 15.5 oz, which is less than 16 oz, but within the range of the standard deviation, we fail to reject the null hypothesis. Therefore, we cannot claim that the soft drink contains less than 16 oz based on this sample.

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