Question

At its peak after the 2007-2008 ​recession, credit card delinquency rates in a certain region reached 6.75​%. Since its​ peak, delinquency rates have declined to a new low of 1.15​% in the second quarter of 2015. You are charged with checking the most recent credit card delinquency rates in the region. Using a random sample of 453 credit card​ customers, you found that 16 were at least 30 days overdue on their monthly payments. Using a 95​% confidence​ interval, can you conclude that the proportion of delinquent card holders changed since its lowest point in 2015​?

Answer 1

Ho:p= 0.0115

Ha:p< 0.0115

alpha=0.05

By 95% confidence interval:

95% confidence interval for p is

p^-z*sqrt(p^(1[p^)/n,p^+z*sqrt(p^(1[p^)/n)

0.03532009-1.96*sqrt(0.03532009*(1-0.03532009)/453),0.03532009+1.96*sqrt(0.03532009*(1-0.03532009)/453)

0.01832163,0.05231855

95% lower limit for p is 0.01832163

95% upper limit for p is 0.05231855

sicne the 95% confidence interval do not contain p=0.0115

Reject null hypothesis

there is sufficient statistical evidence by 95% confidence interval for prportion to conclude that  the proportion of delinquent card holders changed since its lowest point in 2015​