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 R17 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.
The null hypothesis is that there is no change in the mean loan size:
H0: μ = R120,000
The alternative hypothesis is that there is a change in the mean loan size:
H1: μ ≠ R120,000
The null and alternative hypothesis for this test can be defined as follows:
Null hypothesis (H0): The mean loan size has not changed as a result of the change in policy and interest rates. μ = R120,000
Alternative hypothesis (H1): The mean loan size has changed as a result of the change in policy and interest rates. μ ≠ R120,000
Please note that the significance level of 1% corresponds to an alpha value (α) of 0.01.