Question

Consumers with credit scores below 600 have a very difficult time getting approved for car or mortgage loans. Historically 20​% 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 500 people was chosen. From this​ sample, 114 people had credit scores less than 600. Using alpha equals 0.10​

a. construct null and alternate hypothesis

b. determine critical value(s)

c. calculate test statistic

d. calculate P-value

Answer 1

a)

H0: p = 0.20

Ha: p > 0.20

b)

At 0.10 significance level,

Critical value = 1.2816

c)

Sample proportion = 114 / 500 = 0.228

Test statistics

Z = ( - p ) / sqrt [ p( 1 - p) / n ]

= ( 0.228 - 0.20) / sqrt [ 0.20 ( 1 - 0.20) / 500]

= 1.57

d)

p-value = P(Z > z )

= P(Z > 1.57)

= 1 - P(Z < 1.57)

= 1 - 0.9418

= 0.0582

Since p-value < 0.10 significance level, Reject H0.