Answer to Question #115875 in Statistics and Probability for Shane Jessica Ballera

Question

Hypothesis Testing

Red Bull claims that their energy drink only contains 100 calories but you believe otherwise. Thus, you sampled 40 cans of Red Bull and learned that the average calorie content is 110 with a standard deviation of 12 calories. Discuss your findings at α 0.05 using p-value method.

Answer 1

The following null and alternative hypotheses need to be tested:

$H_0:\mu=100$

$H_1:\mu\not=100$

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

Based on the information provided, the significance level is $\alpha=0.05,$ and the critical value for a two-tailed test is $t_c=2.023.$

The rejection region for this two-tailed test is $R=\{t:|t|>2.023\}.$

The t-statistic is computed as follows:

$$t={\bar{X}-\mu\over s/\sqrt{n}}={110-100\over 12/\sqrt{40}}=5.27$$

Using the P-value approach: The p-value is $p=0,$ and since $p=0<0.05,$ it is concluded that the null hypothesis is rejected. Therefore, there is enough evidence to claim that the population mean $\mu$  is different than 100, at the 0.05 significance level.