Question

1. In a random sample of 160 lazy students, 104 believe that resume inflation is not only ethical, but necessary. However, in a random sample of 200 non-lazy students, only 40 believe that resume inflation (ethical or not) is necessary. (a) Construct a 90% confidence interval for the difference between the proportions of the lazy students and of the non-lazy students who believe that resume inflation is necessary. (b) Find the p-value of the test HO: PL = Pn versus H1: Pc > Pn, where pl and pn are the overall proportions of the lazy students and of the non-lazy students who believe that resume inflation is necessary, respectively.

Answer 1

Answer:

a)

Given,

Ho : p1-p2 = 0

Ha : p1-p2 > 0

sample proportion p1^ = x1/n1 = 104/160 = 0.65

p2^ = x2/n2 = 40/200 = 0.2

p = (x1+x2)/(n1+n2) = 0.4

b)

90% CI = (p1^-p2^) +/- z*sqrt(p1^(1-p1^)/n1 + p2^(1-p2^)/n2)

substitute values

= (0.65 - 0.2) +/- 1.645*sqrt(0.65(1-0.65)/160 + 0.2(1-0.2)/200)

= 0.45 +/- 0.0775

= (0.3725 , 0.5275)

test statistic z = (p1^ - p2^)/sqrt(pq(1/n1 + 1/n2))

substitute values

= (0.65 - 0.2)/sqrt(0.4*0.6(1/160 + 1/200))

= 8.66

c)

P value = P(z > 8.66) = 0

Here we observe that, p value < alpha, so we reject Ho.

So there is sufficient evidence to support the claim.