(b) Construct and interpret a 90% confidence interval for the difference between
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Question
(b) Construct and interpret a 90% confidence interval for the difference between the two population proportions, p 28. Course Redesign In many colleges and universities around the country, educators are changing their approach to instructio from a "teacher/lecture-centered model" to a "student-centered model" where students learn in a laboratory environment in which lecture is deemphasized and students can proceed at a pace suitable to their learning needs. In one school where this model was being introduced, of the 743 students who enrolled in the traditional lecture model, 364 passed; of the 567 in the student-centered model, 335 passed. (a) What is the response variable in this study? What is the explanatory variable? (b) Does the evidence suggest that the student-centered mod results in a higher pass rate than the traditional model? U the = 0.05 level of significance.Explanation / Answer
a.The response variable is the focus of a question in a study or experiment,
An explanatory variable is one that explains changes in that variable. It can be anything that might affect the response variable
laboratory experiment done student center model and traditional mode
sample one, x1 =364, n1 =743, p1= x1/n1=0.49
sample two, x2 =335, n2 =567, p2= x2/n2=0.591
b.
Given that,
sample one, x1 =364, n1 =743, p1= x1/n1=0.49
sample two, x2 =335, n2 =567, p2= x2/n2=0.591
null, Ho: p1 = p2
alternate, H1: p1 < p2
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.645
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.49-0.591)/sqrt((0.534*0.466(1/743+1/567))
zo =-3.628
| zo | =3.628
critical value
the value of |z | at los 0.05% is 1.645
we got |zo| =3.628 & | z | =1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: left tail - Ha : ( p < -3.6279 ) = 0.00014
hence value of p0.05 > 0.00014,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 < p2
test statistic: -3.628
critical value: -1.645
decision: reject Ho
p-value: 0.00014
we have enough evidence to support that student centered mode results in the higher pass rate than in traditional mode
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