Chapter 2

The tables that follow report the marital status of 20 respondents in two different apartment complexes. (HINT: Make sure that you have the correct numbers in the numerator and denominator before answering these questions. For example, problem 2.1a asks for "the percentage of respondents in each complex who are married," and the denominators will be 20 for these two fractions. Problem $2.1d$, on the other band, asks for the "percentage of the single respondents who live in Complex $B$," and the denominator for this fraction will be $4+6$, or $10.)$ $$\text{Unknown environment 'tabular'}$$ a. What percentage of the respondents in each complex are married? b. What is the ratio of single to married respondents at each complex? c. What proportion of each sample are widowed? d. What percentage of the single respondents live in Complex B? e. What is the ratio of the "unmarried/living together" to the "married" at each complex?

The town of Shinbone, Kansas, has a population of 211,732 and experienced 47 bank robberies, 13 murders, and 23 auto thefts during the past year. Compute a rate for each type of crime per 100,000 population. (HINT: Make sure that you set up the fraction with size of population in the denominator:)

Sixteen high school students completed a class to prepare them for the College Boards. Their scores were as follows. $\begin{array}{llll}420& 345& 560& 650\\ 459& 499& 500& 657\\ 467& 480& 505& 555\\ 480& 520& 530& 589\end{array}$ These same 16 students were given a test of math and verbal ability to measure their readiness for college-level work. Scores are reported here in terms of the percentage of correct answers for each test. $$\text{Unknown environment 'tabular'}$$ a. Display each of these variables in a frequency distribution with columns for percentages and cumulative percentages. b. Construct a histogram and frequency polygon for these data. c. (This problem is optional.) Find the upper and lower real limits for the intervals you established.

Twenty-five students completed a questionnaire that measured their attitudes toward interpersonal violence. Respondents who scored high believed that in many situations a person could legitimately use physical force against another person. Respondents who scored low believed that in no situation (or very few situations) could the use of violence be justified. $\begin{array}{lllll}52& 47& 17& 8& 92\\ 53& 23& 28& 9& 90\\ 17& 63& 17& 17& 23\\ 19& 66& 10& 20& 47\\ 20& 66& 5& 25& 17\end{array}$ a. Construct a frequency distribution to display these data. b. What are the midpoints of the class intervals? c. Add columns to the table to display the percentage distribution, cumulative frequency, and cumulative percentage. d. Construct a histogram and a frequency polygon to display these data. e. Write a paragraph summarizing this distribution of scores.

A local youth service agency has begun a sex education program for teenage girls who have been referred by the juvenile courts. The girls were given a 20 -item test for general knowledge about sex, contraception, and anatomy and physiology upon admission to the program and again after completing the program. The scores of the first 15 girls to complete the program are as follows. $$\text{Unknown environment 'tabular'}$$ $$\text{Unknown environment 'tabular'}$$ Construct frequency distributions for the pretest and posttest scores. Include a column for percentages. (HINT: There were 20 items on the test, so the maximum range for these scores is $20.$ If you use 10 class intervals to display these scores, the interval size will be 2. Since there are no scores of 0 or 1 for either test, you may state the first interval as $2-3.$ To make comparisons easier, both frequency distributions should have the same intervals.)