Question

Delta Airlines is trying to determine if pilots are deliberately slowing down during a labor dispute. They know that their all their flights have a mean late time of 12.8 minutes with a standard deviation of 4.8 minutes. They took a random sample of 31 flights during the dispute and found they were 14.1 minutes late on average. Using a significance level of 0.05, is there any evidence to back the pilots claim that they are not slowing down?

Answer 1

null hypothesis:Ho μ		=	12.8
Alternate Hypothesis:Ha μ		>	12.8
for 0.05 level with right tail test , critical z=			1.645
Decision rule:reject Ho if test statistic z>1.645
	population mean μ=	12.8
	sample mean 'x̄=	14.100
	sample size    n=	31.00
	std deviation σ=	4.800
	std error ='σx=σ/√n=	0.8621
	test stat z = '(x̄-μ)*√n/σ=	1.51

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

we do not have have sufficient evidence to conclude at 5% level of signfiicance that  to back the pilots claim that they are not slowing down