Question

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. \begin{tabular}{crc} \hline Case & Pretest & Posttest \\ \hline 1 & 5 & 7 \\ \(J\) & 15 & 12 \\ \(K\) & 13 & 20 \\ \(L\) & 4 & 5 \\ \(M\) & 10 & 15 \\ \(N\) & 8 & 11 \\ 0 & 12 & 20 \\ \hline \end{tabular} \begin{tabular}{ccc} \hline Case & Pretest & Posttest \\ \hline A & 8 & 12 \\ B & 7 & 13 \\ C & 10 & 12 \\ D & 15 & 19 \\ E & 10 & 8 \\ F & 10 & 17 \\ G & 3 & 12 \\ H & 10 & 11 \end{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.)

Short answer

Two frequency tables were created each with the following intervals: 2-3, 4-5, 6-7, 8-9, 10-11, 12-13, 14-15, 16-17, 18-19, 20-21. The pretest scores are most frequent in the 10-11 interval (40%), while the posttest scores peak at the 12-13 interval (33.33%).

Step-by-step solution

Collect the Scores

First, gather all the pretest and posttest scores from the table. Here are the scores: Pretest: [5, 15, 13, 4, 10, 8, 12, 8, 7, 10, 15, 10, 10, 3, 10]Posttest: [7, 12, 20, 5, 15, 11, 20, 12, 13, 12, 19, 8, 17, 12, 11]

Define Class Intervals

With the given hint, we use 10 class intervals, each of size 2. The intervals will be: 2-3, 4-5, 6-7, 8-9, 10-11, 12-13, 14-15, 16-17, 18-19, 20-21.

Create Frequency Distribution for Pretest Scores

Count the pretest scores that fall into each interval: 2-3: 14-5: 26-7: 18-9: 210-11: 612-13: 214-15: 116-17: 018-19: 020-21: 0

Calculate Percentages for Pretest Scores

Convert the frequency of pretest scores into percentages:2-3: (1/15) * 100 ≈ 6.67%4-5: (2/15) * 100 ≈ 13.33%6-7: (1/15) * 100 ≈ 6.67%8-9: (2/15) * 100 ≈ 13.33%10-11: (6/15) * 100 ≈ 40%12-13: (2/15) * 100 ≈ 13.33%14-15: (1/15) * 100 ≈ 6.67%16-17: 0%18-19: 0%20-21: 0%

Create Frequency Distribution for Posttest Scores

Count the posttest scores that fall into each interval: 2-3: 04-5: 16-7: 18-9: 110-11: 212-13: 514-15: 216-17: 118-19: 120-21: 1

Calculate Percentages for Posttest Scores

Convert the frequency of posttest scores into percentages:2-3: 0%4-5: (1/15) * 100 ≈ 6.67%6-7: (1/15) * 100 ≈ 6.67%8-9: (1/15) * 100 ≈ 6.67%10-11: (2/15) * 100 ≈ 13.33%12-13: (5/15) * 100 ≈ 33.33%14-15: (2/15) * 100 ≈ 13.33%16-17: (1/15) * 100 ≈ 6.67%18-19: (1/15) * 100 ≈ 6.67%20-21: (1/15) * 100 ≈ 6.67%

Compile the Frequency Distributions into Tables

Organize the frequency distributions and percentages into tables for better comparison:Pretest:| Interval | Frequency | Percentage ||----------|-----------|------------|| 2-3 | 1 | 6.67% || 4-5 | 2 | 13.33% || 6-7 | 1 | 6.67% || 8-9 | 2 | 13.33% ||10-11 | 6 | 40% ||12-13 | 2 | 13.33% ||14-15 | 1 | 6.67% ||16-17 | 0 | 0% ||18-19 | 0 | 0% ||20-21 | 0 | 0% |Posttest:| Interval | Frequency | Percentage ||----------|-----------|------------|| 2-3 | 0 | 0% || 4-5 | 1 | 6.67% || 6-7 | 1 | 6.67% || 8-9 | 1 | 6.67% ||10-11 | 2 | 13.33% ||12-13 | 5 | 33.33% ||14-15 | 2 | 13.33% ||16-17 | 1 | 6.67% ||18-19 | 1 | 6.67% ||20-21 | 1 | 6.67% |

Key concepts

frequency distribution

In statistics, a frequency distribution shows how often each value in a set of data occurs. For example, in the sex education program, the scores of the girls can be grouped into ranges or intervals. This organization helps in identifying patterns.

To create a frequency distribution, you need to:

• List the distinct scores or intervals.
• Count how often each score or interval appears.
• Compile this data into a clear list or chart.

For instance, in the pretest data with intervals of [2-3, 4-5, 6-7, etc.], counting and listing these occurrences will provide an easy overview of the scores distribution.

pretest and posttest scores

Pretest and posttest scores are used to measure knowledge or skill improvements. In this exercise, the girls were tested before (pretest) and after (posttest) the sex education program.

Looking at both sets of scores helps evaluate the program's effectiveness. If posttest scores improve significantly, it suggests the program was successful in teaching the intended material.

To analyze: Compare the scores directly or use techniques like calculating the average increase or creating a frequency distribution for each set.

percentage calculation

Calculating percentages involves expressing a fraction of the total as parts of 100. This helps in understanding proportions at a glance.

From the counts or frequencies, the calculation is straightforward:

• Frequency of the interval / Total number of scores = Proportion
• Proportion × 100 = Percentage

For example, if there are 15 girls and 3 scored in a certain interval:
3 / 15 = 0.2
0.2 × 100 = 20%
This tells us that 20% of the girls scored within that interval.

class intervals

Class intervals are ranges used to group similar data points. They simplify the analysis and understanding of distributions.

For the sex education program scores, intervals like \(2-3\) or \(10-11\) group close scores together. Here are steps to define intervals:

• Determine the range (e.g., 2-21).
• Decide the number of intervals (e.g., 10 intervals).
• Calculate the size of each interval (Range/Number of intervals).

Here, the interval size is 2, making the intervals \(2-3, 4-5, ... , 20-21\).

juvenile court referrals

Juvenile court referrals are cases where youth are directed to court due to offenses or other issues requiring legal intervention. Often, these youths may be assigned to remedial programs as seen in the exercise with the sex education program.

Such programs aim to educate and rehabilitate, reducing future re-offense chances. Evaluating these programs is crucial to ensure they effectively help these youths learn and improve their behavior. This evaluation often involves pretest and posttest assessments to measure knowledge acquisition or behavioral changes post-intervention.