When consumers apply for credit, their credit is rated using the FICO score. A bank manager used a random sample of the credit scores of 18 customers and determined the following 95% confidence interval:
(613.6, 708.0)
If the sample used 45 customers rather than 18 customers, how would you expect the 95% confidence interval to change? Support your answer.
A) The confidence interval would be narrower since the standard error would be smaller due to the larger sample size.
B) The confidence interval would be very similar since we are still estimating FICO scores which have wide variation.
C) Given the confidence level of 95%, the interval calculated using a sample of 44 would be about the same since the confidence is not very high.
D) The confidence interval would be wider since the standard error would be larger due to the larger sample size.