In: Statistics and Probability
Educational economists are trying to determine whether
preschool head-start programs are beneficial in improving reading
proficiency. To...
- 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.
- 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. (5)
- 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. (5)