Question

A company that has two key products for the business wants to estimate the difference between the number of complaints received for each type of product. For this purpose, a statistical study was designed that consists of taking the historical data of monthly complaints that occurred for each product in the last 48 months, in three different points of sale chosen completely random. The results are shown below:

Type of product	A	B
Average of registered complaints	17.2	25.1
Standard deviation	4.6	5.3

The company wants to verify that the average number of complaints received for product A is greater than 15, using a significance level of 0.05. Calculate the p-Value. What conclusions do you reach?

Answer 1

null hypothesis: HO: μ		=	15
Alternate Hypothesis: Ha: μ		>	15
0.1 level with right tail test and n-1= 47 df, critical t=			1.300		from excel: t.inv(0.9,47)
Decision rule :reject Ho if test statistic t>1.3
	population mean μ=		15
	sample mean 'x̄=		17.200
	sample size    n=		48
	std deviation s=		4.6000
	std error ='sx=s/√n=4.6/√48=		0.6640
	t statistic ='(x̄-μ)/sx=(17.2-15)/0.664=		3.313
	p value      =		0.001		from excel: tdist(3.313,47,1)

since p value <0.05 ; we reject null hypothesis

we have sufficient evidence to conclude that the average number of complaints received for product A is greater than 15.