Day 21 AGENDA: Rev Ch 3 and 4.1---20 minutes Begin Ch 4.2

Advanced Placement Statistics Section 4.2: Relationships Between Categorical Variables EQ: How do you use a two-way table to determine relationships between 2 categorical (qualitative) variables?

Recall: Relationships Between Two Quantitative Variables Scatterplots Association Regression

Relationships Between Two Qualitative Variables Contingency Tables

Terms To Know: Marginal Totals --- counts for each row and column

255 students stated that they were not stressed about school.

Terms To Know: Marginal Distributions --- percent for each row and column

37 / 419 ≈8.83% 8.83% of the students complained about having acid-reflux.

Terms To Know: Marginal Totals --- counts for each row and column Marginal Distributions --- percent for each row and column Joint Distributions --- percent involving more than one variable

131 / 419 ≈31.3% 31.3% of these students said they were under stress but did not have acid-reflux.

Terms To Know: Marginal Totals --- counts for each row and column Marginal Distributions --- percent for each row and column Joint Distributions --- percent involving more than one variable Conditional Distributions ---percent for one variable across some condition on the other variable

4/255 ≈1.7% 1.7% of the non-stressed students complained of having acid-reflux.

131/ 382 ≈34.3% 34.3% of the students said they were stressed given that they did not have acid-reflux.

Now answer the questions on your notes. What is the probability a person responded they felt under stress? 164/ 419 ≈39.1% What is the probability that a person responded they felt under stress and had reflux? 33/ 419 ≈7.9% What is the probability that a person with reflux responded they felt under stress? 33/ 37 ≈89.2% What is the probability that a person under stress responded they had reflux? 33/ 164 ≈20.1%

The following two-way table reports data on all undergraduate students enrolled in U.S. colleges and universities in the fall of 1995 whose age was known. 286 7,771 4,388 1,672 1,966 3,473 6,119 2,559 14,117 1. Calculate the marginal totals. Place them in the table. 2. How many undergraduate students were enrolled in colleges and universities? 14,117,000

0.003 0.009 0.005 0.003 0.0203 0.098 0.085 0.326 0.042 0.5545 0.0303 0.101 0.086 0.094 0.311 0.008 0.051 0.016 0.043 0.118 0.139 0.246 0.433 0.181 1.00 3. Calculate the relative frequency for each data value and place it in the table.

4. What percent of the undergraduate students were 18 to 24 years old in the fall of the academic year? 7771 out of 14117 = 55.1% 5. What is one comparison you can make about undergraduate college enrollment in Fall 1995? Almost twice as many students were enrolled as 4 yr full-time at 43% than 2-yr part-time at 23%. 6. Find the percent of undergraduates enrolled in each of the four types of program who were 18 to 24 years old. Make a bar graph to compare the results. Why do you think we chose this age group?

Type of College Student Distribution of 18 to 24 year olds in College During Fall 1995 .6 2 yr Full time: 1378/7771 = 17.73% .5 .4 2 yr Part time: 1198/7771 = 15.42% .3 Relative Frequency .2 4 yr Full time: 4607/7771 = 59.28% .1 4 yr Part time: 588/7771 = 7.57% 2 yr. 2 yr. 4 yr. 4 yr. Fulltime Parttime Fulltime Parttime Type of College Student

5. What is one comparison you can make about undergraduate college enrollment in Fall 1995? Almost twice as many students were enrolled as 4 yr full-time at 43% than 2-yr part-time at 23%. 6. Find the percent of undergraduates enrolled in each of the four types of program who were 18 to 24 years old. Make a bar graph to compare the results. Why do you think we chose this age group? 7. What is one comparison you can make about college enrollment of 18 to 24 yr olds in Fall 1995?

Distribution of 18 to 24 year olds in College During Fall 1995 More than half, 59%, of all 18 to 24 year olds are enrolled in 4 yr. colleges full time than in the other programs. Almost twice as many 18 to 24 year olds, attend 2 yr. colleges part time, as those who attend 4 yr. colleges part time, 15% to 8% respectively.

8. An association of two-year colleges asks: “What percent of students enrolled part-time at 2-year colleges are 25 to 39 years old?” 1427 out of 3473 = 41% 9. A bank that makes education loans to adults asks: “What percent of all 25- to 39- year-old students are enrolled part-time at 2-year colleges?” 1427 out of 4388 = 33%

11. What is one comparison you can make from the table in #10? 10. Create a contingency table relating the conditional distributions of college program given age. 41/286 = 14% 125/286 = 44% 75/286 = 26% 45/286 = 16% 1378/7771 = 18% 1198/7771 = 15% 4607/7771 = 59% 588/7771 = 8% 428/4388 = 10% 1427/4388 = 33% 1212/4388 = 28% 1321/4388 = 30% 119/1672 = 7% 723/1672 = 43% 225/1672 = 14% 605/1672 = 36% 11. What is one comparison you can make from the table in #10? 12. Explain the difference in the information you provided for #5, #7, and #11.

Remember, no single graph portrays the form of the relationship Remember, no single graph portrays the form of the relationship. And no single numerical measure summarizes the strength of the association. ASSIGNMENT: p. 298 - 299 #23 – 26 p. 303 #31 – 34