You are given the following information of a company that produces cola fizzy drinks. The
company states that the mean caffeine content per bottle of a fizzy drink is 40 mg with a
standard deviation of 7.5 mg. The quality controller is convinced that it is lower. A sample of
30 randomly drawn bottles has a mean caffeine content of 39.2 mg. Can the quality
controller reject the claim? Conduct a hypothesis test at 0.05 level of significance.
The following null and alternative hypotheses need to be tested:
This corresponds to a left-tailed test, for which a z-test for one mean, with known population standard deviation will be used.
Based on the information provided, the significance level is and the critical value for a left-tailed test is
The rejection region for this left-tailed test is
The z-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is not rejected.
Using the P-value approach:
The p-value is and since it is concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population mean
is less than 40, at the significance level.
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