Hypothesis testing and p-values | Inferential statistics | Probability and Statistics | Khan Academy | Summary and Q&A

TL;DR

A neurologist tests the effect of a drug on response time in rats and determines that the drug has a significant effect.

Key Insights

• 🥳 The experiment shows that the drug has a significant effect on response time in rats.
• ❓ The null hypothesis assumes no effect, while the alternative hypothesis suggests an effect.
• 😘 The probability of obtaining the observed results if the null hypothesis is true is very low.

Transcript

A neurologist is testing the effect of a drug on response time by injecting 100 rats with a unit dose of the drug, subjecting each to neurological stimulus and recording its response time. The neurologist knows that the mean response time for rats not injected with the drug is 1.2 seconds. The mean of the 100 injected rats response times is 1.05 se... Read More

Questions & Answers

Q: What are the two hypotheses used in the experiment?

The null hypothesis assumes that the drug has no effect on response time, while the alternative hypothesis suggests that the drug does have an effect.

Q: How does the neurologist decide whether to accept the alternative hypothesis?

The neurologist calculates the probability of obtaining the observed results if the null hypothesis is true. If this probability is very low (typically below 5%), the alternative hypothesis is accepted.

Q: What is the significance of the Z-score in this analysis?

The Z-score measures the number of standard deviations away from the mean the observed result is. In this case, the result is 3 standard deviations below the mean.

Q: What is the P-value in this analysis?

The P-value is the probability of obtaining a result as extreme as or more extreme than the observed result if the null hypothesis is true. In this case, the P-value is 0.003.

Summary & Key Takeaways

• The neurologist conducts an experiment on 100 rats to test the effect of a drug on response time.

• The mean response time for rats not injected with the drug is 1.2 seconds.

• The mean response time for the 100 rats injected with the drug is 1.05 seconds, indicating that the drug has an effect on response time.