Question

Please explain and show work.

A sample of 1200 firms rated Ba found that 5.6% of these firms defaulted within a year.

a. Test the null hypothesis that the true defect rate is 5% against the alternative that it is different from 5%.

b. What is the p‐value for the test statistic in part a?

Answer 1

Solution :

Given that,

= 0.05

1 - = 0.95

n = 1200

Point estimate = sample proportion = = 0.056

This a two- tailed test.

The null and alternative hypothesis is,

Ho: p = 0.05

Ha: p 0.05

Test statistics

z = ( - ) / *(1-) / n

= ( 0.056 - 0.05) / (0.05*0.95) / 1200

= 0.927

b)

P-value = 2 * P(Z > 0.927 )

= 2 * ( 1 - P(Z < 0.927 ))

= 2 * ( 1 - 0.8256)

= 0.3488