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Chapter 4: Problem 39

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?

Short Answer

Expert verified
For part (a), the 200 mg caffeine group's performance is statistically significant compared to the placebo group. For part (b), the 300 mg group's performance is not statistically significant compared to the 200 mg group.

Step by step solution

01

Understand the Probability and Null Hypothesis

In research, the null hypothesis posits that there is no effect or difference between groups. If the p-value is less than the significance level (commonly 0.05), the null hypothesis is rejected, indicating the result is statistically significant.
02

Interpret the Probability for Part (a)

For part (a), the probability that the difference between the coffee group (200 mg) and the placebo group is due to chance is 0.049. Since 0.049 < 0.05, this result is statistically significant. This means it is very unlikely that the observed difference is due to chance.
03

Formulate Conclusion for Part (a)

Conclude that the 200 mg caffeine group performed better on the memory test compared to the placebo group, and this difference is statistically significant.
04

Interpret the Probability for Part (b)

For part (b), the probability that the higher dose group (300 mg) performed better than the 200 mg group due to chance is 0.75. Since 0.75 > 0.05, this result is not statistically significant. This means the higher dose group's performance is likely due to chance.
05

Formulate Conclusion for Part (b)

Conclude that the higher dose of 300 mg does not show a statistically significant improvement over the 200 mg dose, as the difference could be attributed to chance.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Null Hypothesis
In scientific research, a **null hypothesis** is a statement suggesting there is no effect or no difference between two groups being compared. For example, in a memory study, the null hypothesis might state that caffeine has no effect on memory performance. Researchers test this hypothesis to determine if there is enough evidence to suggest the alternative鈥攖hat caffeine does indeed affect memory.
P-Value Interpretation
A **p-value** helps us understand the probability that the observed results are due to chance. In the study mentioned, the p-value of 0.049 means there is a 4.9% probability that the difference in memory performance between groups occurred by chance. If the p-value is below a threshold (commonly set at 0.05), we consider the results statistically significant. Therefore, a p-value of 0.049 would lead us to reject the null hypothesis, indicating that caffeine likely has an effect on memory.
Caffeine Dosage Effects
The study examines different **dosages of caffeine** and their impact on memory. Participants consuming 200 mg of caffeine showed better memory performance compared to the placebo group. However, when the dosage increased to 300 mg, the performance did not show significant improvement over the 200 mg group. This implies that higher caffeine dosage may not necessarily lead to better memory performance.
Memory Test Performance
In this study, participants underwent a **memory test** to measure the effect of caffeine. It's important to note that performance on memory tests can be influenced by various factors, including the amount of caffeine intake. The study found significant improvement with 200 mg of caffeine compared to no caffeine. However, a further increase to 300 mg did not result in statistically significant improvement, suggesting a possible optimal dose for memory enhancement.
Probability in Research
Understanding **probability** is crucial in research to interpret the likelihood of results occurring by chance. A probability of 0.049 indicates there's a 4.9% chance that the results are due to random variation. This low probability helps researchers conclude that the observed effect (improved memory performance with 200 mg caffeine) is likely real. Conversely, a probability of 0.75 for the difference between 300 mg and 200 mg caffeine suggests a 75% chance that it's due to randomness, indicating no meaningful difference worth noting.

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Most popular questions from this chapter

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