Question

the department of Maternal studies at HSP university coaims that the length of human pregnancy is exactly 270 days. A random sample od 100 pregnancies has a mean of 280 days with a standars deviation of 15 days. Is there enough evidence to support the HSP university's claim at alpha = 0.01?

Answer 1

since sample size is large ; we can use large sample distribution

null hypothesis:Ho μ		=	270
Alternate Hypothesis:Ha μ		≠	270
for 0.01 level with two tail test , critical z=			2.576	(from excel:normsinv(0.005)
Decision rule:reject Ho if absolute test stat|z|>2.576
	population mean μ=		270
	sample mean 'x̄=		280.000
	sample size    n=		100
	std deviation σ=		15.00
	std error ='σx=σ/√n=15/√100=		1.500
	z statistic= ='(x̄-μ)/σx=(280-270)/1.5=		6.67

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to reject the HSP university's claim.