AP Statistics Chapter 12 Section 2

Proportion of successes in the first sample Proportion of successes in the second sample Use p-hat in place of both p-hat 1 and p-hat 2 in the expression for standard error -- this is called the pooled sample proportion

TestConfidence IntervalFormulasAssumptions 1-sample z-test mean SRS Normal pop. Or large n (n>40) Know 1-sample t-test mean (could also be used for a matched pairs design) SRS < very normal 15 < n < can be used except in the presence of outliers or strong skewness > use regardless of normality 2-sample z-test SRSs Normal pops or n>40 2-sample t-test SRS < very normal 15 < < 40 can be used except in the presence of outliers or strong skewness > use regardless of normality 1-proportion SRS from a pop of interest Pop > 10(n) Test of Sign. C.I. 2-proportion SRS from a pop of interest Pop > 10(n) Test of Sign. & CI

Do Preschool programs for poor children make a difference in later life? 62 children enrolled in a preschool in the late 1960s and a control group of 61 similar children who were not enrolled. At 27 years of age, 38 of the preschool group and 49 of the control group had required the help of a social service agency (mainly welfare) in the previous 10 years. Does this provide significant evidence that preschool reduces the later need for social services?

Group 1 is the group who did not attend preschool. Group 2 is the group who did attend preschool. Assumptions: 1.SRSs of populations of interest 2.Population of children preschool age > 10(61+62) = 1230

P = Given that the proportion of people who attended preschool and the proportion of people who did not attend preschool have the same need later in life for social services the observed difference in the two samples would occur approximately 1 out of every 100 times just by chance. Therefore, this statistically significant evidence rejects that attending preschool makes no difference. We are 95% confident that the percent needing social services is somewhere between 3.3% and 34.7% lower among people who attended preschool.

North Carolina State University looked at the factors that affect the success of students in a required chemical engineering course. Students must get a C or better in the course in order to continue as chemical engineering majors. There were 65 students from urban or suburban backgrounds, and 52 of these students succeeded. Another 55 students were from rural or small-town backgrounds; 30 of these students succeeded in the course. Is there good evidence that the proportion of students who succeed is different for urban/suburban versus rural/small-town backgrounds? ( )

Group 1: Students who come from a urban or suburban backgrounds Group 2: Students who come from a rural or small-town backgrounds Assumptions: 1.SRS of pop of interest All students enrolled in a specific class created the sample. 2.Population of Chemical Engineering majors > 10(chemical engineering students enrolled in this class) Given that the proportion of success is the same between the two groups of students the observed difference would occur approx. 3 times out of every 1000 just by chance. Therefore, this statistically significant evidence rejects that the proportion of success is the same between the two groups of students. 90% (.11723,.39186) We are 90% confident that the proportion of success differs somewhere between 11.7% and 39.2% for these two groups of students.