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Example: Would You Pay Higher Prices to Protect the Environment? In 2000, the GSS asked: Are you willing to pay much higher prices in order to protect the environment?

2 Example: Would You Pay Higher Prices to Protect the Environment? In 2000, the GSS asked: Are you willing to pay much higher prices in order to protect the environment? Of n = 1154 respondents, 518 were willing to do so Find a point estimate of the true proportion willing to do so at the time of the survey Find and interpret a 95% confidence interval for the population proportion of adult Americans willing to do so at the time of the survey

3 A recent survey asked: During the last year, did anyone take something from you by force? Of 987 subjects, 17 answered yes Find the point estimate of the proportion of the population who were victims Find the 95% CI for the true population proportion.

4 Full Example: Are Astrologers Predictions Better Than Guessing? Scientific test of astrology experiment: For each of 116 adult volunteers, an astrologer prepared a horoscope for each person and each adult subject also filled out a California Personality Index Survey For a given adult, his or her birth data and horoscope were shown to an astrologer together with the results of the personality survey for that adult and for two other adults randomly selected from the group The astrologer was asked which personality chart of the 3 subjects was the correct one for that adult, based on his or her horoscope; 28 astrologers were randomly chosen to take part in the experiment, and they got 40 correct. The National Council for Geocosmic Research claimed this was larger than 1/3.

5 P VALUE

6 Can Dogs Detect Cancer by Smell? Investigate if dogs can be trained to distinguish a patient with bladder cancer by smelling compounds released in the patient s urine Each of 6 dogs was tested with 9 trials. In each trial, one urine sample from a bladder cancer patient was randomly place among 6 control urine samples In a total of 54 trials with the six dogs, the dogs made the correct selection 22 times (a success rate of 0.407) Does this study provide strong evidence that the dogs predictions were better or worse than with random guessing?

7 Population proportion testing Normally, a pair of dice comes up 7 or 11 with probability p=.222. We watch a craps game for a long time, and count 53 occurrences of a 7 or 11 in 200 rolls. Are the dice loaded?

8 population proportion test 2701 women took folic acid, 35 had major birth defects. For women who do NOT take folic acid, it is known that the rate of birth defects is Does taking folic acid have an effect?

9 Another example (for the men) It is known that the rate of prostate cancer in men is We do a survey, and find 22,000 men who had a vasectomy. 113 of the men of those men got prostate cancer Is there an increased risk?

Example: Aspirin, the Wonder Drug Subjects were 22,071 male physicians Every other day, study participants took either an aspirin or a placebo The

10 Example: Aspirin, the Wonder Drug Subjects were 22,071 male physicians Every other day, study participants took either an aspirin or a placebo The physicians were randomly assigned The study was double-blind: the physicians did not know which pill they were taking, nor did those who evaluated the results

Example: Is TV Watching Associated with Aggressive Behavior? Various studies have examined a link between TV violence and aggressive behavior by those who watch a lot of TV.

12 Example: Is TV Watching Associated with Aggressive Behavior? Various studies have examined a link between TV violence and aggressive behavior by those who watch a lot of TV. A study sampled 707 families in two counties in New York state and made follow-up observations over 17 years. The data shows levels of TV watching along with incidents of aggressive acts. Aggressive Act TV Watching Yes No Total Less than 1 hour per day At least 1 hour per day

13 Biased Lending? In October, 1991, The Association of Community Organizations for Reform Now (ACORN) presented their findings on refusals in mortgage lending to the 102nd Congress. Refusal rates were determined from 200 applications each for white and minority applicants in 20 large national banks. The refusal rates for white and minority applicants were 16% and 36%, respectively. At the 1% significance level, do the data provide sufficient evidence to conclude that, in 1991, the refusal rate in mortgage lending was higher for minority applicants than for white applicants?

14 Example problem A marketing survey involves product recognition in New York and California. Of 558 New Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product. At the 0.05 significance level, do the data provide sufficient evidence to conclude that the recognition rate in New York differs from the recognition rate in California?

106 = = = ( ) The single tail is p value = = both tails

106 = = = ( ) The single tail is p value = = both tails Section 4: Comparing Proportions ) In the 980's, a simple random sample of 84 job applicants revealed that 5 of them had lied on their resumes. In the 2000's, a SRS of 06 revealed that 2 had lied on their