10. A university is concerned about the proportion of students that graduate. To address the issue,...

10. A university is concerned about the proportion of students that graduate. To address the issue, it does the following. First, it gets a random sample of incoming students. Some of the students in this random sample will be required to have extra meetings with a series of advisors and some will not. It randomly decides which of the students will have this requirement and which will not. In the data, 516 of the 885 students that had this requirement graduated, and 444 of the 845 students that did not have this requirement graduated. The university wants to know if this requirement changed the proportion of students who graduate.

(a) What is the null hypothesis and what is the alternative hypothesis?

(b) What is the sample proportion for group 1? (round to 5 digits after the decimal place)

(c) What is the sample proportion for group 2? (round to 5 digits after the decimal place)

(d) What is the pooled estimator for p? (round to 5 digits after the decimal place)

(e) What is the standard error for the difference in the sample proportions? (Use ˜σp1−p2 and round to 5 digits after the decimal place.)

(f) What is the value of the test statistic? (Round to 2 digits after the decimal place.)

(g) What is the p-value of the test? (Round to 3 digits after the decimal place.)

(h) Do we reject or not reject the null hypothesis at the .05 level of significance? Reject Not reject

(i) Can we interpret the difference in the population proportions as a causal effect? Yes, it has a causal interpretation. or No, it does not have a causal interpretation.

Expert Solution

10.

Given that,
sample one, x1 =516, n1 =885, p1= x1/n1=0.583
sample two, x2 =444, n2 =845, p2= x2/n2=0.525
null, Ho: p1 = p2
alternate, H1: p1 != p2
level of significance, α = 0.05
from standard normal table, two tailed z α/2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (p1-p2)/√(p^q^(1/n1+1/n2))
zo =(0.583-0.525)/sqrt((0.555*0.445(1/885+1/845))
zo =2.41
| zo | =2.41
critical value
the value of |z α| at los 0.05% is 1.96
we got |zo| =2.41 & | z α | =1.96
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 2.41 ) = 0.016
hence value of p0.05 > 0.016,here we reject Ho
ANSWERS
---------------
a.
null, Ho: p1 = p2
alternate, H1: p1 != p2
b.
sample one, x1 =516, n1 =885, p1= x1/n1=0.583
c.
sample two, x2 =444, n2 =845, p2= x2/n2=0.525
d.
pooled proportion =2.41
e.
standard error = sqrt( p1 * (1-p1)/n1 + p2 * (1-p2)/n2 )
where
p1, p2 = proportion of both sample observation
n1, n2 = sample size
standard error = sqrt( (0.5831*0.4169/885) +(0.5254 * 0.4746/845))
=0.0239
f.
test statistic: 2.41
critical value: -1.96 , 1.96
g.
p-value: 0.016
h.
decision: reject Ho
i.
we have enough evidence to support the claim that the difference in the population proportions as a causal effect.

orchestra answered 2 years ago

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