First Semester Final Exam The curve on the final was + 4 points (+ 8%) After the curve the statistics for the final are: Mean 43.5 (87%) SD 7.4 Median 45 (90%) Q1 39 Q3 49

Second Semester Overview Chapter 8 – Confidence Intervals Chapter 9 – Significance Tests Chapter 10 – Comparing Two Populations Chapter 11 – Chi Square Tests Chapter 12 – Inference for Regression AP Test is on May 16!

Calculating a Confidence Interval Imagine we took a survey of 55 randomly selected Leland students and found that 31 of them went out of town sometime during the holidays. 1) Determine a 95% confidence interval for p, the proportion of all students who went out of town during the holidays (Use p = 0.5 to calculate the standard deviation).

Create a Confidence Interval You will flip a coin 40 times and record the number of heads. Make your penny land on the carpet each flip! 1) What is the mean and standard deviation for the sampling distribution of “p hat” (samples of 40 coin flips)? 2) Determine “p hat” for your experiment and a 95% confidence interval estimate for p. 3) Write your confidence interval on the board.

Create a Confidence Interval – page 2 4) How many confidence intervals captured the population proportion p? 5) How many confidence intervals did you expect to capture p in a class of 34 students?

Example According to a 2004 paper, 26% of all criminal cases in the U.S. are decided in favor of the defendant. Imagine we take a random sample of 200 cases and find that 43 are decided in favor of the defendant. 1) What is the standard deviation of the sampling distribution? 2) Are the conditions for constructing a confidence interval met? Explain. 3) Based on our sample, construct a 95% confidence interval estimate for p, the proportion of all cases decided in favor of the defendant.

Practice A simple random sample of 411 students at a large public university found the mean time spent studying for a final exam was 7.74 hours. Assume we know the standard deviation of the number of hours spent studying for a final exam by all students is 3.4 hours. 1) What is the standard deviation of the sampling distribution? 2) Are the conditions for constructing a confidence interval met? Explain. 3) Construct a 95% confidence interval estimate for m, the mean time spent studying for a final exam by all students at the university.