It is known that the mean size of commercial loans made by a certain bank has been R120 000 in the recent past. Anew 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. If we were to test at a 1% significance level whether there is a change in the mean loan size or not, give the value of alpha.
1 answer
In hypothesis testing, alpha (α) is the significance level, which is the probability of rejecting the null hypothesis when it is actually true. In this case, you mentioned that the bank wants to test whether the mean loan size has changed, which corresponds to a two-tailed test.
Since the significance level is given as 1%, this means:
\[ \alpha = 0.01 \]
This value of alpha indicates that there is a 1% risk of concluding that the mean loan size has changed when, in fact, it has not.
