Question

Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 38 defaulted loans. If the critical value for z is -1.282 and the observed value is -1.74, the appropriate decision is to _______.

		reduce the sample size
		increase the sample size
		reject the null hypothesis
		fail to reject the null hypothesis
		do nothing

Answer 1

The null and alternative hypotheses are

H0:p 0.05

H1:p>0.05

p:true population proportion of default in personal loans

We reject null hypothesis when obsd Z>critical value.

Obsd value here, is less than critical value, so we fail to reject the null hypothesis.

But note that, obsd value of Z as per the information comes as:

So please check your calculations of observed and critical value. This test will be a right tailed test.

As per your information the answer is provided.

If there is any understanding problem regarding this please feel free to ask any doubt in comment box. Thank you.