Reference no: EM132495239

1. Educational economists are trying to determine whether preschool head-start programs are beneficial in improving reading proficiency. To test the effect they conducted a lottery with 100 parents of preschool kids who indicated that they wanted to send their kids to a head-start program but couldn't afford it. The researchers randomly selected 36 students from the 100 and gave them a voucher for preschool. All 36 of these students attended a head-start program. After attending head-start, and then 3 years of elementary school, all 100 students were administered a reading test. Of the 36 who attended head-start, 29 passed the test. Of the 64 who did not attend head-start, 48 passed.

a. Using a significance level of 5%, conduct a hypothesis test to determine whether the head-start program affected the proportion of students who successfully pass the reading test.

b. Based on your response to a., does this mean that we can state definitively that there really is or isn't an effect of preschool on reading ability after grade 3? I am interested in having you explain using the statistical interpretation of hypothesis testing (as opposed to critiquing the experimental design.