Question

The present software produces 6% mistakes in interpreting customers' needs. Using a new software, in a random sample of 500 customers we had 25 mistakes. Does the new software produce fewer mistakes? Test at the .05 level of significance.

Answer 1

null Hypothesis:              Ho:   p=		0.06
alternate Hypothesis:    Ha: p <		0.06

for 0.05 level and left tailed test , critical z=			-1.645
Decision rule :   reject Ho if test statistic z < 1.645
sample success x   =		25
sample size          n    =		500
std error σp =√(p*(1-p)/n) =		0.0106
sample proportion p̂ = x/n=		0.0500
z =(p̂-p)/σp=(0.05-0.06)/0.05=		-0.94

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that new software produce fewer mistakes