Ap Statistics Inference Test Review

AP STATISTICS INFERENCE TEST REVIEW

1. About 130,000 high school students took the AP Statistics exam in 2010. The free-response section of the exam consisted of five open-ended problems and an investigative task. Each free-response question is scored on a 0 to 4 scale (with 4 being the best). For one of the problems, a random sample of 30 student papers was taken. The mean score for this sample is and the standard deviation is Construct and interpret a 99% confidence interval to estimate the mean score on this question.

2. A random sample of 100 of a certain popular car model last year found that 20 had a certain minor defect in the brakes. The car company made an adjustment in the production process to try to reduce the proportion of cars with the brake problem. A random sample of 350 of this year’s model found that 50 had the minor brake defect. Was the company’s adjustment successful? Carry out an appropriate test to support your answer.

3. How quickly do synthetic fabrics such as polyester decay in landfills? A researcher buried polyester strips in the soil for different lengths of time, then dug up the strips and measured the force required to break them. Breaking strength is easy to measure and is a good indicator of decay. Lower strength means the fabric has decayed. For one part of the study, the researcher buried 10 strips of polyester fabric in well-drained soil in the summer. The strips were randomly assigned to two groups: 5 of them were buried for 2 weeks and the other 5 were buried for 16 weeks. Here are the breaking strengths in pounds: Group 1 (2 weeks): 118 126 126 120 129 Group 2 (16 weeks): 124 98 110 140 110

Do the data give good evidence that polyester decays more in 16 weeks than in 2 weeks? Carry out an appropriate test to help answer this question.

4. Baby walkers are seats hanging from frames that allow babies to sit upright with their legs dangling and feet touching the floor. Walkers have wheels on their legs that allow the infant to propel the walker around the house long before he or she can walk or even crawl. Typically, babies use walkers between the ages of 4 months and 11 months. Because most walkers have tray tables in front that block babies’ views of their feet, child psychologists have begun to question whether walkers affect infants’ cognitive development. One study compared mental skills of a random sample of those who used walkers with a random sample of those who never used walkers. Mental skill scores averaged 113 for 54 babies who used walkers (standard deviation of 12) and 123 for 55 babies who did not use walkers (standard deviation of 15). Is there evidence that the mean skill score is different between the two groups? Explain your answer.

5. A study of “adverse symptoms” in users of over-the-counter pain relief medications assigned subjects at random to one of two common pain relievers: acetaminophen and ibuprofen. In all, 650 subjects took acetaminophen, and 44 experienced some adverse symptom. Of the 347 subjects who took ibuprofen, 49 had an adverse symptom. Does the data provide convincing evidence that the two pain relievers differ in the proportion of people who experience an adverse symptom? Support your conclusion with a test of significance. Use a significance level of 0.05.