Question

Proctor & Gamble claims that at least half the bars of Ivory soap they produce are 99.44% pure (or more pure) as advertised. Unilever, one of Proctor & Gamble's competitors, wishes to put this claim to the test. They sample the purity of 145 bars of Ivory soap. They find that 62 of them meet the 99.44% purity advertised.

What is the P Value?

Answer 1

null Hypothesis:               Ho:   p		>=0.5
alternate Hypothesis:    Ha: p		<0.5
for 0.05 level with left tailed test , critical z=-1.645
Decision rule :   reject Ho if test statistic z < 1.645
sample success x   =		62
sample size          n    =		145
std error   se =√(p*(1-p)/n) =		0.0415
sample proportion p̂ = x/n=		0.4276
test stat z =(p̂-p)/√(p(1-p)/n)=		-1.74
p value                          =		0.0409 (from excel)normsdist(-1.74) function)

(please try 0.0406 if required unrounded z score for p value)