It is known that the mean size of commercial loans made by a certain bank has been R120 000 in the recent past. A new change in the credit policy allows larger amounts be borrowed, but the interest rate is now 2% higher than in the recent past. The bank wants to test if the mean loan size has changed as a result of the change in policy and interest rates. A random sample of 144 commercial loans made since these changes yields a mean loan size of R100 000 with a standard deviation of R20 000. The null and alternative hypothesis are given by _____, if we were to test at a 1% significance level whether there is a change in the mean loan size or not.

Answer 1

To set up the hypotheses for the given scenario, we need to establish the null hypothesis (H0) and the alternative hypothesis (H1).

1. Null Hypothesis (H0): This represents the statement of no effect or no change. In this case, it states that the mean loan size has not changed from the previously known value of R120,000. Therefore, we set: \[ H_0: \mu = 120,000 \]

2. Alternative Hypothesis (H1): This represents the statement indicating that an effect or a change exists. Since the bank wants to test if the mean loan size has changed, it can be either greater than or less than the previously known mean. Thus, we set: \[ H_1: \mu \neq 120,000 \]

In summary, the hypotheses to test at a 1% significance level whether there has been a change in the mean loan size are:

• Null Hypothesis (H0): \(\mu = 120,000\)
• Alternative Hypothesis (H1): \(\mu \neq 120,000\)

This is a two-tailed test since we are looking for any change (either increase or decrease) in the mean loan size.