Detailed answer data are available as an Excel file.

There are two sets of 95% confidence intervals you can construct.

The first is simply the sample mean plus or minus two standard deviations. In this case, these intervals are as follows:

• minority: 5.7 to 49.4
• white: -1.7 to 24.3

These intervals are 95% confidence intervals for the range of refusal rates among the banks reported here. These intervals overlap quite a bit. This means that the actual refusal rate for minorities is sometimes below that of whites in the data covering all the banks reported here. However, in looking at the data, you can see that this never happens at any one bank. Looking at each bank, one at a time, is a case of paired comparison, and it seems that paired comparison makes sense in this case.

The second is the sample mean plus or minus two standard errors, which yields the following intervals:

• minority: 22.6 to 32.4
• white: 8.4 to 14.2

These intervals are 95% confidence intervals for the average overall refusal rate. These intervals do not overlap. If we assume that the banks reported here are a random sample of all metropolitan banks, there is good reason to believe that, in general, minorities are refused loans more often than whites. This conclusion is also justified if you use t-tests to look at the data. Excel can perform a paired comparison t-test or a regular t-test. The simple form of the t-test covered on p. 169 of The Cartoon Guide to Statistics gives another result. The values for the t-statistic are as follows:

• paired t-test: t = 8.94
• regular t-test: t = 5.70
• simple t-test: t = 4.59

This shows, as observed above, that a paired comparison seems to indicate a greater difference than a non-paired comparison. But in either case, the statistical significance is very large. The probability that these two data sets represent two samples of the same population is very, very small.

However, it is a big leap from statistical significance to racial discrimation. There are many other factors which could explain the difference in refusal rates. Again, for further discussion of these issues, see www.hud.gov/offices/fheo/lending/fairlend.cfm and www.clev.frb.org/research/com/081596.htm.