Question

A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. Assume the population standard deviation is known to be 5.6 days.

a.	State the null and alternative hypotheses.
b.	Using a critical value, test the null hypothesis at the 5% level of significance.
c.	Using a p-value, test the hypothesis at the 5% level of significance.
d.	What type of error may have been committed for this hypothesis test?

Answer 1

a)

null hypothesis:Ho		μ	<=	15
Alternate Hypothesis:Ha		μ	>	15

b)

for 0.05 level with right tailed test , critical value of z=				1.645
Decision rule :                   reject Ho if test statistic z>1.645
	population mean	μ=	15
	sample mean	x̄=	16.20
	sample size	n=	49.00
	population std deviation	σ=	5.600
	standard errror of mean =	σx=σ/√n=	0.8000
	test statistic           z             =	(x̄-μ)/σx=	1.50

as test statistic is below critical value 1.645 we can not reject null hypothesis

c)

for above test statistic and right tailed test, p value =0.0668

as p value is greater than 0.05 level , we can not reject null hypothesis

d)

as we fail to reject null hypothesis, we might have commited a type II error , if null hypothesis is false i.e company deliver your carpet in more than 15 days