Calculating confidence interval for difference of means | AP Statistics | Khan Academy

TL;DR

Calculate a 90% confidence interval for the difference in mean body temperature after exercising for 30 and 60 minutes.

Transcript

• [Instructor] Kylie suspected that when people exercise longer, their body temperatures change. She randomly assigned people to exercise for 30 or 60 minutes, then measured their temperatures. The 18 people who exercised for 30 minutes had a mean temperature, so this is the sample mean for that sample of 18 folks, of 38.3 degrees Celsius, with a s... Read More

Key Insights

• 🏃 Kylie's experiment compares the mean body temperature of individuals who exercise for 30 and 60 minutes.
• 🏃 The sample mean body temperature for the 30-minute exercise group is 38.3 degrees Celsius.
• 🏃 The sample mean body temperature for the 60-minute exercise group is 38.9 degrees Celsius.
• 🏃 The confidence interval for the mean body temperature difference after exercising for the two durations is calculated using the t interval formula.
• 😃 The critical t value for a 90% confidence interval was found using the conservative degrees of freedom.
• 👥 The sample standard deviations and sample sizes of both groups were used to calculate the estimate of the sampling distribution of the difference in sample means.
• ❓ The final confidence interval calculation is done by substituting the values into the formula.

Questions & Answers

Q: What did Kylie suspect about body temperatures and exercise duration?

Kylie suspected that people's body temperatures change when they exercise for longer durations.

Q: How many participants were assigned to the 30-minute exercise group?

There were 18 participants in the 30-minute exercise group.

Q: What is the formula for calculating the confidence interval for the difference in mean body temperature?

The formula is: difference between sample means ± critical t value * square root of [(sample standard deviation of group A)^2 / sample size of group A + (sample standard deviation of group B)^2 / sample size of group B].

Q: How did Kylie determine the critical t value for a 90% confidence interval?

Kylie used the conservative degrees of freedom, which was one less than the smaller sample size (18), and looked it up in a t table to find the critical t value of 1.74.

Summary & Key Takeaways

• Kylie conducted an experiment to study the effects of exercise duration on body temperature for 30 and 60 minutes.

• The mean body temperature for the 30-minute exercise group was 38.3 degrees Celsius, with a standard deviation of 0.27 degrees Celsius.

• The mean body temperature for the 60-minute exercise group was 38.9 degrees Celsius, with a standard deviation of 0.29 degrees Celsius.