A study on the enhancing effect of coffee on long-term...

A study on the enhancing effect of coffee on long-term memory found that 35 participants given $200 \mathrm{mg}$ of caffeine performed better on a memory test 24 hours later compared to the placebo group that received no caffeine. a. There was a probability of $0.049$ that the difference between the coffee group and the placebo group was due to chance. What do you conclude? b. A group given a higher dose of $300 \mathrm{mg}$ performed better than the $200 \mathrm{mg}$ group, with a probability of $0.75$ that this difference is due to chance. What do you conclude?

A study on the enhancing effect of coffee on long-term memory found that 35 participants given $200 \mathrm{mg}$ of caffeine performed better on a memory test 24 hours later compared to the placebo group that received no caffeine.
a. There was a probability of $0.049$ that the difference between the coffee group and the placebo group was due to chance. What do you conclude?
b. A group given a higher dose of $300 \mathrm{mg}$ performed better than the $200 \mathrm{mg}$ group, with a probability of $0.75$ that this difference is due to chance. What do you conclude?

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Key Concepts

P-value

The p-value is a statistic that helps researchers determine the probability of observing an effect at least as extreme as the one found in the study, assuming that the null hypothesis is true. It is used to quantify the evidence against the null hypothesis by measuring the likelihood that the observed result is due solely to chance.

Statistical Significance

Statistical significance is a determination that an observed effect or difference in a study is unlikely to have occurred by chance, based on a predefined significance level (typically 0.05). When a result is statistically significant, it suggests that there is enough evidence to support the idea that the effect is real rather than being the result of random variation.

Null Hypothesis Testing

Null hypothesis testing is a methodological framework in statistics where the default assumption is that there is no effect or difference between the groups being compared. Researchers use the p-value to assess whether the observed data are sufficiently inconsistent with this null hypothesis, thus providing grounds for its rejection in favor of an alternative hypothesis.

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