Caffeine in a cola

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A brand of cola is sampled n=40 times. The mean caffeine is 19.57 mg per 6 oz serving and the sample standard deviation is 1.40 mg. The claim under test is that the mean is 19 mg, against the alternative that it is higher.

1. State the model and the two hypotheses.

2. Give the test statistic and its null distribution.

3. Compute the observed statistic, the one-sided p-value, and the decision at level 0.05. Use the fact that the upper tail of t_{39} beyond 2.57 is about 0.007.

Worked answer (click to show)

The model is an independent normal sample. The hypotheses are H_0:\mu=19 against H_1:\mu>19. The statistic (\overline X-19)/(s/\sqrt n) is t_{39} under H_0. The observed value is

\frac{19.57-19}{1.40/\sqrt{40}}=2.57.

The one-sided p-value is 0.007, so H_0 is rejected at level 0.05. The mean caffeine in this brand is higher than 19 mg per serving.