Question

A sample of 18 California wine specimens found a mean lead content of 287 parts per billion (ppb) with a standard deviation of 120 ppb. At the 1% level of significance can we show that the mean lead content of all California wines is not 240 ppb?

(a) State and test appropriate hypotheses. State conclusions



(b) What assumption is necessary for the analysis above to be appropriate?

Answer 1

a)

null hypothesis: HO: μ		=	240
Alternate Hypothesis: Ha: μ		≠	240
0.01 level with two tail test and n-1= 17 df, critical t=				2.898
Decision rule :reject Ho if absolute value of test statistic|t|>2.898
	population mean μ=	240
	sample mean 'x̄=	287.000
	sample size   n=	18.00
	sample std deviation s=	120.000
	std error 'sx=s/√n=	28.284
	test stat t ='(x-μ)*√n/sx=	1.662

since test statistic does not falls in rejection region we fail to reject null hypothesis
we do not have have sufficient evidence to conclude that  mean lead content of all California wines is not 240 ppb

b)

we need to assume that sample observations are independent and population is normally distributed since sample size is small ( <30)