Question

In a recent satisfaction survey of 400 customers at XYC inc., it is found that proportion of customers who are completely satisfied is 0.28. Test the hypothesis that the proportion of customers who are completely satisfied is different from 0.26 at 0.05 level of significance.

Answer 1

null Hypothesis:              Ho:   p=		0.260
alternate Hypothesis:    Ha: p ≠		0.260
for 0.05 level and two tailed test , critical z=			1.96	(from excel:normsinv(0.025)
Decision rule :   reject Ho if absolute value of test statistic |z|>1.96

sample success x   =		112
sample size          n    =		400
std error σp =√(p*(1-p)/n) =		0.0219
sample prop p̂ = x/n=112/400=		0.2800
z =(p̂-p)/σp=(0.28-0.26)/0.28=		0.91

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 population proportion differs from 0.26.