Mathematics 376 – Probability and Statistics II Discussion Day – Specifying Tests of Hypotheses March 17, 2006

Background

Last time we introduced some basic terminology about statistical tests of hypotheses – the null hypothesis H_{0}, the alternative hypothesis H_{a}, test statistic, the rejection region RR, and the Type I and Type II errors and their probabilities, α and β respectively.

Discussion Questions

Each group – You have 20 minutes to analyze your assigned situation to identify H_{0}, H_{a} for a conjectural test that could be used address the issue raised. Also identify a test statistic that you could compute from your samples, and which has a known distribution, at least approximately (i.e. one of the ones fo which we have tables in the text – standard normal, t, χ^{2}, F, etc.) Say what distribution your test statistic has. When you are done, put up your results on the board. If you have time, think about some of the others too.

Group 1. It is claimed that the proportion of adult Americans who select jogging as one of their recreational activities is 30%. You are the public health department of Sedentaria, a bedroom and retirement community outside a major city and you want to determine if the proportion in your town is actually lower. You plan to conduct a survey of 500 randomly selected adults to help answer the question.

Group 2. A previous survey showed that 20% of the drivers in New Bumpshire, a state without a mandatory seat-belt law, always wear seat-belts even though it is not required. You are the New Bumpshire State Police and you have now instituted public-service TV ads that are designed to shock people into using seat-belts by showing gruesome auto accidents where the drivers were seriously injured. After the ads have been on the air for 2 months, to determine whether they are increasing the proportion of drivers using their seat-belts, you randomly stop 500 drivers and determine whether they are using their seat-belts.

Group 3. You are staff members of Update, a national newsmagazine that has conducted a telephone poll of 800 adult Americans, 605 of them smokers. The respondents were asked: “Should the Federal tax on cigarettes be raised by $1.25 to help pay for health care reform?” You want to determine whether the proportion of non-smokers who say yes is different from the proportion of smokers who say yes.

Group 4. The FVC (forced vital capacity) is the amount of air that a person can force out of his/her lungs in one exhalation. The population mean FVC for adults is about 3.4 liters, and the FVC is normally distributed. You are the coaching staff of a college volleyball team. You want to assess the general physical fitness of your team members by measuring their FVC’s to determine whether they are above average. You test all 11 team members.

Group 5. The mean birth weight of babies in the US is 3315 grams, and the birth weight is normally distributed, with standard deviation 300 grams. You are a biostatistical research team in Ghana trying to decide whether mean birth weights in your country are different from those in the US. You will have data from 1000 births to use to make the comparison.

Group 6. You are the statistical team at BigState U’s School of Agriculture and Veterinary Medicine. You want to study the variability of the number of pounds of butterfat produced by your herd of Holstein cows in the 305-day milking period after the birth of a calf. You have data on the butterfat production for 100 cows, and you want to compare your herd’s performance with that of Northeastern Southwest U’s herd, which had σ^{2} = 140.

Group 7. You are the quality-control team for DC Dullco, an auto parts manufacturer. You regularly select self-sealing stembolts from the production line and subject them to a torque test. The goal is for the mean torque at failure of the stembolts to equal 125. You select 100 stembolts one day, test them, and want to determine if the goal is being met.

Group 8. You are a social psychology research team at the Center for Advanced Social Studies. In the past, it was believed that 40% of women think all men are basically selfish. You want to determine whether the number is larger now. You will design a survey and interview 200 women to determine what they think.