Question

Question 11 O ponts A group of young businesswomen 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 $25,000 $22,000 $24,000 $27,000 $26,000 $26,000 $28.000 $23,000 $24,000 Assume the population of incomes is normally distributed. Compute the sample mean and the standard deviation. State the hypotheses for this problem. Compute the test statistic. At 95% confidence using the p-value approach, what is your conclusion? d. :3 (12pt) T--E T TT Arial dddt

Answer 1

a) Let's compute the mean and standard deviation first:

Income (X)	X-mu	(X-mu)^2
28000	3000	9000000
24000	-1000	1000000
26000	1000	1000000
25000	0	0
23000	-2000	4000000
27000	2000	4000000
26000	1000	1000000
22000	-3000	9000000
24000	-1000	1000000
225000		30000000

Mean = 225000/9 = 25000

Standard deviation = SQRT(30000000/8) = 1936.492

b) Ho: mu <= 25000

Ha: mu > 25000

c) Test statistic is:

t = (25000 - 25000)/(1936.942/3) = 0

d) At t = 0, p-value = 0.5

As p=0.5 > 0.05, we cannot reject the null hypothesis.

Hence, we conclude that we do not have enough evidence to say that the average income is atleast 25000