Question

A group of young business women wish to open a high fashion boutique in a vacant store but only if the average income of households in the area is at least 25,000. A random sample of 9 households showed the following results.

$28,000 $24,000 $26,000 $25,000

$23,000 $27,000 $26,000 $22,000

$24,000

Assume the population of income is normally distributed. Using the critical value approach, test the hypothosis at the 5% level of significance.

Answer 1

null hypothesis: Ho:             μ		=	25000
Alternate Hypothesis: Ha:μ		<	25000
0.05 level with right tailed test and n-1= 8 df, critical t=			1.860
Decision rule :                   reject Ho if test statistic t>1.860
	population mean μ=	25000
	sample mean         x=	25000.00
	sample size             n=	9
	sample std deviation s=	1936.492
	std error sx=s/√n=	645.4972
	test stat t='(x-μ)*√n/s=	0.00

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 average income of households in the area is less than 25000