Objective: Construct confidence intervals for means Homework: Pages 542‐543: # 11—15 Warm‐up: 1‐Proportion Inference Exam t‐distribution: Chapter 23 Day 1 Confidence Intervals: 1. Residents are concerned that vehicles traveling on Lakeville Avenue often exceed the posted speed limit of 30 miles per hour. The local police decide to place a radar speed detector by the side of the road, and as a vehicle approaches, their speed will be displayed. The police hope this will cause drivers to slow down. The following data represent the speed of 23 randomly selected cars passing by the radar detector: 29 29 24 34 34 34 34 32 36 28 31 31 30 27 34 29 37 36 38 29 21 31 26 Construct a 90% confidence interval for the mean speed of vehicles traveling on Lakeville Avenue. 2. As part of their final project in AP Statistics, 2 students randomly selected 18 rolls of a generic brand of toilet paper to measure how well this brand could absorb water. To do this, they poured ¼ cup of water onto a hard surface and counted how many squares it took to completely absorb the water. Here are the results from their 18 rolls: 29 20 25 29 21 24 27 25 24 29 24 27 28 21 25 26 22 23 Construct and interpret a 99% confidence interval for  = the mean number of squares of generic toilet paper needed to absorb 1/4 cup of water. 3. A professor at a large university randomly samples 24 students, and asks how many credits they are taking for the semester. The following table shows the results: 12 13 14 14 15 15 15 16 16 16 16 16 17 17 17 18 18 18 18 19 19 19 20 21 Find the 95% confidence interval for the number of credits taken by the students at the university. 4. Textbook authors must be careful that the reading level of their book is appropriate for the target audience. Some methods of assessing reading level require estimating the average word length. The following represents the word length of 20 randomly selected words from our textbook. 5 5 2 11 1 5 3 8 5 4
7 2 9 4 8 20 5 6 6 6
a. Construct a 98% confidence interval for the average word length of the textbook. b. For a better estimate, an editor wants to estimate the text’s mean word length to within 0.5 letters with 98% confidence. How many selected words does she need to use? 5. The principal at a large high school claims that students spend at least 10 hours per week doing homework, on average. To investigate this claim, an AP Statistics class selected a random sample of 250 students from their school and asked them how long they spent doing homework during the last week. The sample mean was 10.2 hours and the sample standard deviation was 4.2 hours. Construct and interpret a 95% confidence interval for the mean time that students at this school spent doing homework in the last week. Based on your interval what can you conclude about the principal’s claim?