Behavioral Statistics

For each problem, Download the data from the Problem Description (see below).  Calculate all appropriate descriptive statistics; Conduct all tests employing a 5% significance level.

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License records in a county reveal that 15% of cars are subcompacts (1), 25% are compacts (2), 40% are midsize (3), and the rest are an assortment of other styles and models (4). A random sample of accidents involving cars licensed in the county was drawn. The type of car was stored in the file using the codes in parentheses. Can we infer at the 5% significance level that certain sizes of cars are involved in a higher than expected percentage of accidents?

Datafile:

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During the past decade many cigarette smokers have attempted to quit. Unfortunately, nicotine is highly addictive. Smokers employ a large number of different methods to help themselves quit. These include nicotine patches, hypnosis, and various forms of therapy. A researcher for the Addiction Research Council wanted to determine why some people are able to quit while others who attempted to quit failed. He surveyed 1,000 people who planned to quit smoking. He determined their educational level and whether, 1 year later, they continued to smoke. Educational level was recorded in the following way.

    1 = did not finish high school
    2 = high school graduate
    3 = university or college graduate
    4 = completed a postgraduate degree

A continuing smoker was recorded as 1; a quitter was recorded as 2. These data are stored in columns 1 (education level) and 2 (continuing smoker?) in the file. Can we infer at the 5% significance level that the amount of education is a factor in determining whether a smoker will quit?

Datafile:

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According to NBC News (11 March, 1994) more than 3,000 Americans quit smoking each day. (Unfortunately, more than 3,000 Americans start smoking each day.) Because nicotine is one of the most addictive drugs, quitting smoking is a difficult and frustrating task. It usually takes several tries before success is achieved. There are various methods, including cold turkey, nicotine patch, hypnosis, and group therapy sessions. In an experiment to determine how these methods differ, a random sample of smokers who have decided to quit was selected. Each smoker chose one of the methods listed above. After 1 year the respondents reported whether they have quit (2 = yes and 1 = no) and which method they used (1 = cold turkey; 2 = nicotine patch; 3 = hypnosis; 4 = group therapy sessions). These data are stored in columns 1and 2, respectively in file . Is there sufficient evidence at the 5% significance level to conclude that the four methods differ in their success?

A newspaper publisher, trying to pinpoint his market’s characteristics wondered whether the way people read a newspaper is related to the reader’s educational level.  A survey asked adult readers which section of the paper they read first and asked them to report their highest educational level. These data were recorded and stored in file .

        Column 1: first section read where 1 = front page, 2 = sports, 3 = editorial, and 4 = other
        Column 2: educational level where 1 = did not complete high school, 2 = high school graduate, 3 = university or college graduate,
and 4 = postgraduate degree

What do these data tell the publisher at the 1% significance level about how educational level affects the way adults read the newspaper?

Every week the Florida lottery draws 6 numbers between 1 and 49. Lottery ticket buyers are naturally interested in whether certain numbers are drawn more frequently than others. To assist players the Sun-Sentinel publishes the number of times each of the 49 numbers has been drawn in the past 52 weeks. The numbers and the frequency with which each occurred are stored in columns 1 and 2, respectively, in the file . These data are from the Sunday, 4 January, 2009 edition.

        a. If the numbers are drawn from a uniform distribution, what is the expected frequency for each number?
        b. Can we infer at the 5% significance level that the data were not generated from a uniform distribution?

The relationship between drug companies and medical researchers is under scrutiny because of possible conflict of interest. The issue that started the controversy was a 1995 case control study that suggested that the use of calcium-channel blockers to treat hypertension led to an increased risk of heart disease. This led to an intense debate both in technical journals and in the press.  Researchers writing in the New England Journal of Medicine (“Conflict of Interest in the Debate over Calcium Channel Antagonists,” 8 January, 1998, p. 101) looked at the 70 reports that appeared during 1996—1997, classifying them as favorable, neutral, or critical toward the drugs. The researchers then contacted the authors of the reports and questioned them about financial ties to drug companies. The results are stored in the file in the following way.

        Column 1: results of the scientific study where 1 = favorable, 2 = neutral, 3 = critical

        Column 2: 1 = financial ties to drug companies, 2 = no ties to drug companies

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© David M. Compton, Ph.D.
Last updated: December 7, 2009