Question

Smartphone Users. A Ring Central survey of 380 smartphone users showed that 152 of them said that theirsmartphone is the only thing they could not live without. Use a 0.01 significance level to test the claim thatfewer than half of smartphone users identify the smartphone as the only thing they could not live without

Answer 1

null Hypothesis:              Ho:   p=		0.500
alternate Hypothesis:    Ha: p <		0.500
for 0.01 level and left tailed test , critical z=			-2.33	(from excel:normsinv(0.01)
Decision rule :   reject Ho if test statistic z < 2.33

sample success x   =		152
sample size          n    =		380
std error σp =√(p*(1-p)/n) =		0.0256
sample prop p̂ = x/n=152/380=		0.4000
z =(p̂-p)/σp=(0.4-0.5)/0.026=		-3.90

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that fewer than half of smartphone users identify the smartphone as the only thing they could not live without