Solutions to Homework #11
(W4150 ‘Intro to Probability and Statistics’, S04)
Sec. 10.12. (1)
H
0
: p = .4
H
1
: p > .4
α
= .05
If we denote the number of those who choose lasagne by X then under H
0
X ~ binomial(20;.4) and so
Pvalue is given by P[X >
9  p = .4] = 1 – P[X <
8  p = .4] = .4044 > .05
Therefore we cannot reject nullhypothesis.
Sec.10.12. (2)
H
0
: p = .4
H
1
: p > .4
α
= .05
Let’s denote the number of those who favored capital punishment by X. Then under H
0
X ~
binomial(15;.4) and so Pvalue is given by P[X >
8  p = .4] = 1 – P[X <
7  p = .4] =
= .2131 > .05
Therefore we cannot reject nullhypothesis.
Sec. 10.12. (6)
H
0
: p = .25
H
1
: p > .25
α
= .05
Since n = 90 > 30 we’d like to use normal approximation for binomial distribution here.
μ
= np = 22.5;
σ
=
√
npq = 4.107 and critical region is defined as X >
28 where X is the number of
students using bicycles. Therefore critical value of Z is z = (28.5 – 22.5)/(4.107) = 1.43 and P[X >
28] = P[Z > 1.43] = 1  .9236 = .0724 > .05
formally we cannot reject H
0
; however, relatively
low Pvalue clearly indicates that there is some evidence in favor of alternative hypothesis.
Sec. 10.12 (9)
H
0
: p
1
= p
2
H
1
: p
1
≠
p
2
, where p
1
is proportion of urban residents and p
2
– proportion of suburban residents
who favor the nuclear plant.
Following Example 10.12 we compute
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '04
 GALLEGO
 Null hypothesis, Probability theory, Statistical hypothesis testing, critical region

Click to edit the document details