Question

A hospital director is told that 31% of the treated patients are uninsured. The director wants to test the claim that the percentage of uninsured patients is less than the expected percentage. A sample of 380 patients found that 95 were uninsured. Make the decision to reject or fail to reject the null hypothesis at the 0.05 level. a. reject null hypotheses or b. fail to reject null hypotheses

Answer 1

null Hypothesis:              Ho:   p=		0.310
alternate Hypothesis:    Ha: p <		0.310
for 0.05 level and left tailed test , critical z=			-1.645	(from excel:normsinv(0.05)
Decision rule :   reject Ho if test statistic z < 1.645
sample success x   =		95
sample size          n    =		380
std error σp =√(p*(1-p)/n) =		0.0237
sample prop p̂ = x/n=95/380=		0.2500
z =(p̂-p)/σp=(0.25-0.31)/0.024=		-2.53

since test statistic falls in rejection region we reject null hypothesis

option A is correct : reject null hypotheses