Math 119 Chapter 9 part 3

The script begins with an introduction to the topic of matched pairs hypothesis testing, found in chapter 9.3 of the book and 9.4 in the notes. The instructor clarifies that they will not cover the final section of the homework due to time constraints. The focus is on methods for testing claims about population differences using matched pairs of sample values, often representing before and after scenarios. The process involves calculating the difference between the two values and using these differences for hypothesis testing and constructing confidence intervals. The instructor emphasizes that the approach will be consistent with previous chapters, transforming a two-sample problem into a one-sample problem by calculating the differences between the pairs.

The second paragraph delves into the specifics of calculating the mean difference between matched pairs, denoted as d-bar, and using it for hypothesis testing. The null hypothesis (H0) typically states that there is no significant difference (mu_d equals zero), while the alternative hypothesis (Ha) varies based on the claim being tested. The instructor demonstrates how to calculate d-bar using a set of temperatures, both actual and predicted, and how to perform a t-test using a calculator. The process includes entering the differences into the calculator, finding the standard deviation, and computing the test statistic to determine if the forecast is accurate.

In this paragraph, the instructor applies the hypothesis testing method to determine if there is sufficient evidence to conclude that the mean difference in weather forecasts is not zero, indicating forecast accuracy. The data provided includes actual and predicted low temperatures for five days. The instructor guides through the process of calculating the sum of differences, finding the sample mean difference (d-bar), and setting up the hypothesis test. The test statistic is computed, and a p-value is determined, leading to the conclusion that there is insufficient evidence to claim the forecasts are inaccurate, as the p-value is greater than the significance level (alpha = 0.05).

The script continues with an example of testing the superstition that Friday the 13th is unluckier, using data on hospital admissions due to motor vehicle crashes. The hypothesis is that there is a higher average of crashes on Friday the 13th compared to the sixth. The instructor shows how to calculate the mean difference and perform a one-tailed t-test, given the negative differences indicating fewer accidents on the 13th. The resulting p-value is found to be 0.021, leading to the rejection of the null hypothesis and acceptance of the alternative, suggesting that Friday the 13th is indeed associated with a higher average of crashes.

The final paragraph of the script discusses constructing a confidence interval to test for the existence of a mean difference. Using the matched pairs approach, the instructor demonstrates how to calculate the confidence interval for the differences in accidents between two Fridays. The confidence interval is computed using the t-interval function on the calculator, yielding a range that includes zero. According to the guidelines for hypothesis testing with confidence intervals, if zero is within the interval, it indicates that there is not enough evidence to claim a significant difference between the means, thus the null hypothesis that there is no difference cannot be rejected.

The instructor concludes the video by summarizing the activities covered in the video, which focused on the end of chapter nine and the notes. They mention that they have chosen not to cover certain sections to save time and encourage students to reach out for help if needed. The video serves as a final review for the concepts of matched pairs hypothesis testing and confidence intervals, aiming to clarify the process and calculations involved.