Question

Question 5 of 7 tpoint) Attempt 1 of Unlimited View question in a popup 8.3 Section Exercise 18 ( p a c) Good credit: The Fair Isaac Corporation (FICO) credit score is used by banks and other lenders to determine whether someone is a good credit risk. Scores range from 300 to 850, with a score of 720 or more indicating that a person is a very good credit risk. An economist wants to determine whether the mean FICO score is lower than the cutoff of 720. She finds that a random sample of 40 people had a mean FICO score of 680 with a standard deviation of 90. Can the economist conclude that the mean FICO score is less than 7207 Use the a=0.01 level of significance and the P-value method with the TI-84 Plus calculator. Part: 0 / 4 Part 1 of 4 State the appropriate null and alternate hypotheses. This hypothesis test is a (Choose one) v test.

Answer 1

5.

Given that,
population mean(u)=720
sample mean, x =680
standard deviation, s =90
number (n)=40
null, Ho: μ=720
alternate, H1: μ<720
level of significance, α = 0.01
from standard normal table,left tailed t α/2 =2.426
since our test is left-tailed
reject Ho, if to < -2.426
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =680-720/(90/sqrt(40))
to =-2.8109
| to | =2.8109
critical value
the value of |t α| with n-1 = 39 d.f is 2.426
we got |to| =2.8109 & | t α | =2.426
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :left tail - Ha : ( p < -2.8109 ) = 0.00384
hence value of p0.01 > 0.00384,here we reject Ho
ANSWERS
---------------
null, Ho: μ=720
alternate, H1: μ<720
test statistic: -2.8109
critical value: -2.426
decision: reject Ho
p-value: 0.00384
we have enough evidence to support the claim that mean FICO score is less than 720