Question

You want to know if caffeine improves performance on a repetitive task composed of 100 words. From a normal distribution, you randomly selected a group of 64 participants who received 10 mg of caffeine 30 min before being tested. You want to know if your treatment is effective at the threshold of 0.05. It is known that the average population is 18.8 with a standard deviation of 5.0 for this type of test. Show your reasoning. Do not forget to include hypotheses and the decision.

Results:

26 16 15 10 13 15 15 18 20 13 20 17 17 13 15 25 24 12 15 12 23 19 24 15 18 26 25 20 21 12 18 19 15 17 12 18 23 17 19 8 14 22 22 19 17 14 13 17 18 21 21 15 14 9 15 11 21 23 14 16 18 11 18 25

Answer 1

Sample size = n = 64

Sample mean = = 17.3125

Population standard deviation = = 5

Claim: The treatment is effective.

The null and alternative hypothesis is

Level of significance = 0.05

Here population standard deviation is known so we have to use z-test statistic.

Test statistic is

Critical value = 1.96    ( Using z table)

Critical value < Test statistic | z | we reject the null hypothesis.

Conclusion:

The treatment is not effective.