Consumers with credit scores below 600 have a very difficult time getting approv

Question

Consumers with credit scores below 600 have a very difficult time getting approved for car or mortgage loans. Historically 21% of people had a credit score below 600. Due to the recent financial crisis, the federal government is concerned that this proportion has increased. To test this hypothesis, a random sample of 100 people was chosen. From this sample, 27 people had credit scores less than 600, Using =0.10, complete parts a and b below a. Does this sample provide support for the government's concern that the proportion of people with credit scores below 600 has increased? Determine the null and alternative hypotheses. Choose the correct answer below OA. Ho p> 0.21 H ps0.21 C. Ho :pa:021 Hp 0.21 O B. Ho:p=0.21 H1 : p 0.21 D. Ho p20.21 H p

Explanation / Answer

Given that,
possibile chances (x)=27
sample size(n)=100
success rate ( p )= x/n = 0.27
success probability,( po )=0.21
failure probability,( qo) = 0.79
null, Ho:p=0.21  
alternate, H1: p>0.21
level of significance, = 0.1
from standard normal table,right tailed z /2 =1.28
since our test is right-tailed
reject Ho, if zo > 1.28
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.27-0.21/(sqrt(0.1659)/100)
zo =1.4731
| zo | =1.4731
critical value
the value of |z | at los 0.1% is 1.28
we got |zo| =1.473 & | z | =1.28
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: right tail - Ha : ( p > 1.47309 ) = 0.07036
hence value of p0.1 > 0.07036,here we reject Ho
ANSWERS
---------------
null, Ho:p=0.21
alternate, H1: p>0.21
critical value: 1.28
test statistic: 1.47
decision: reject Ho, Reject H0. There is sufficient evidence that the proportion of
people with credit scores below 600 has increased
p-value: 0.07036

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