TESTING HYPOTHESES ABOUT PROPORTIONS CHAPTER 20

ESSENTIAL CONCEPTS Hypothesis testing involves proposing a model, then determining if the data we observe is consistent with the model or so unusual that we must reject it. The claim being assessed is called the null hypothesis (H 0 ). It is usually a statement of “no change”, “no effect”, or “no difference”. The null hypothesis must specify a value for some population parameter. The alternative hypothesis (H A ) proposes what we should conclude if we find the null hypothesis to be unlikely. The p-value is the probability that we get the value we observed, given that the null hypothesis is true. A small p- value indicates that the observation is improbable and calls into question the validity of H 0. We never “accept” the null hypothesis. We either fail to reject it (when the p-value is large) or reject it (when p- value is small.)

A 1996 report from the U.S. Consumer Product Safety Commission claimed that at least 90% of all American homes have at least one smoke detector. A city’s fire department has been running a public safety campaign about smoke detectors consisting of posters, billboards, and ads on radio and TV and in the newspaper. The city wonders if this concerted effort has raised the local level above the 90% national rate. Building inspectors visit 400 randomly selected homes and find that 376 have smoke detectors. Is this strong evidence that the local rate is higher than the national rate?

There are supposed to be 20% orange M&M’s. Suppose a bag of 122 has only 21 orange ones. Does this contradict the company’s 20% claim?

#13 According to government statistics, in % of students had not been absent from school at all during a selected month. In 2000, responses from 8302 students showed that this had slipped to 33%. Do these figures give evidence of declining student enrollment? Write appropriate hypotheses. Check the assumptions and conditions. Perform the test and find the p-value. State your conclusion. Do you believe the difference is meaningful?

29. An airline claims that it rarely loses passengers’ luggage. It further claims that when it is lost, 90% of luggage is found and delivered to its owner within 24 hours. A consumer group surveyed a large number of travelers and found that only 103 out of 122 people who lost luggage on the airline were reunited with their luggage within 24 hours. Does this cast doubt on the airline’s claim?