Question

Calculate the test statistic and p-value for each sample. Use Appendix C-2 to calculate the p-value. (Negative values should be indicated by a minus sign. Round your test statistic to 3 decimal places and p-value to 4 decimal places.)

	Test Statistic		p-value
(a) H0: ππ ≤ .55 versus H1: ππ > .55, α = .05, x = 56, n = 86
(b) H0: ππ = .30 versus H1: ππ ≠ .30, α = .05, x = 20, n = 39
(c) H0: ππ ≥ .10 versus H1: ππ < .10, α = .01, x = 7, n = 103

Answer 1

A)

sample success x   =		56
sample size          n    =		86
std error σp =√(p*(1-p)/n) =		0.0536
sample prop p̂ = x/n=56/86=		0.6512
z =(p̂-p)/σp=(0.651-0.55)/0.054=		1.886
p value                          =		0.0296	(from excel:1*normsdist(-1.886)

(please try 0.0297 if this comes wrong)

B)

sample success x   =		20
sample size          n    =		39
std error σp =√(p*(1-p)/n) =		0.0734
sample prop p̂ = x/n=20/39=		0.5128
z =(p̂-p)/σp=(0.513-0.3)/0.073=		2.900
p value                          =		0.0037	(from excel:2*normsdist(-2.9002547149)

C)

sample success x   =		7
sample size          n    =		103
std error σp =√(p*(1-p)/n) =		0.0296
sample prop p̂ = x/n=7/103=		0.0680
z =(p̂-p)/σp=(0.068-0.1)/0.03=		-1.084
p value                          =		0.1392	(from excel:1*normsdist(-1.083862206)