Question

Acredit score is used by Credil agencies (such as mortgage companies and banks) to assess the creditworthiness of individuals. Values range from 300 to 850, with a credit score over 700 considered to be a quality credit risk. According to a survey, the mean credit score is 7075. A credit analyst wondered whether high-income individuals (incomes in excess of S100.000 per year) had higher credit scores. He obtained a random sample of 38 high income individuals and found the sample mean credit score to be 726.7 with a standard deviation of 81.2 Conduct the appropriate test to determine high-income individuals have higher credit scores at the a=0.05 level of significance. State the rull and alternative hypotheses. H = 7075 H > 7075 (Type Integers or decimal. Do not round) Mentify the last 6-Round to two decimal places as needed.) Idently the value P-value-Round to three decimal places as needed.) Make a conclusion regarding the hypothesis Fail to reject the nullypothesis. There is not wicient evidence to claim at the mean credit score of high-income individuals a greater than 7075

Answer 1

null hypothesis: HO: μ		=	707.5
Alternate Hypothesis: Ha: μ		>	707.5

population mean μ=		707.5
sample mean 'x̄=		726.700
sample size    n=		38
std deviation s=		81.2000
std error ='sx=s/√n=81.2/√38=		13.1724
t statistic ='(x̄-μ)/sx=(726.7-707.5)/13.172=		1.46

p value      =

0.077

from excel: tdist(1.458,37,1)

Fail to reject Ho; there is not sufficient evidence,,,,,,,,is greater than 707.5

b)

	Pop 1	Pop 2
sample mean x =	26.900	16.300
std deviation s=	4.800	3.300
sample size n=	200	200

for 90 % CI & 199 df value of t=		1.653	from excel: t.inv(0.95,199)
margin of error E=t*std error                   =		0.681
lower bound=mean difference-E     =		9.919
Upper bound=mean differnce +E      =		11.281

option B is correct

b)

option D is correct