Confidence interval for hypothesis test for difference in proportions | AP Statistics | Khan Academy

TL;DR

A university conducted a study comparing the passing rates of in-person and online courses, using a confidence interval to estimate the difference. The interval included zero, indicating no significant difference in passing rates.

Transcript

• [Narrator] A university offers a certain course that students can take in-person or in an online setting. Teachers of the course were curious if there was a difference in the passing rate between the two settings. Data from a recent semester showed that 80% of students passed the in-person setting and 75% of students passed the online setting. Th... Read More

Key Insights

• ☠️ The passing rates for in-person and online courses were 80% and 75%, respectively.
• ☠️ A confidence interval of -0.04 to 0.14 was estimated for the difference in passing rates.
• ☠️ The researchers assumed the null hypothesis that the true difference in passing rates is zero.
• ❓ The confidence interval included the assumed difference, indicating no significant difference.
• 😀 The P value, which measures the probability of observing the results, was greater than the significance level of 5%, resulting in a failure to reject the null hypothesis.

Questions & Answers

Q: What was the purpose of the study?

The purpose was to determine if there was a significant difference in passing rates between in-person and online courses.

Q: How did the researchers analyze the data?

The researchers used a 95% confidence interval to estimate the difference in passing rates and test their null hypothesis.

Q: What is the significance level used in traditional hypothesis tests?

The significance level is typically set at 5%, indicating a 5% probability of getting the observed results if the null hypothesis is true.

Q: What does it mean if the confidence interval includes the assumed difference from the null hypothesis?

If the confidence interval includes the assumed difference (usually zero) from the null hypothesis, it suggests that there is no significant difference between the two groups.

Summary & Key Takeaways

• The study compared the passing rates of in-person and online courses at a university.

• Data from a recent semester showed that 80% of students passed in-person courses, while 75% passed online courses.

• Using a 95% confidence interval, the researchers estimated the difference in passing rates to be between -0.04 and 0.14, indicating no significant difference.