What you did for means in the previous chapter you can also do for proportions. When finding a proportion different from an expected proportion, you want to test whether the proportion found is significantly different from the proportion expected.

Figure 5.42 helps explain this concept. You perform three different tests a one-tailed test at the lower end, a one-tailed test at the higher end, and a two-tailed test:

• In a sample of 60 vaccinated cases, you found 16 anthrax infections ("yes," or "success") versus 44 non-infected cases so p=27%:

  • The null hypothesis claims no effect from vaccination, so p=50% in cell I4. It claims that 27% is a random deviation from 50% due to sample size.

  • The alternative hypothesis claims that vaccination has a lowering effect. Therefore, you need to test only at one tail the lower tail ( p<5%). It claims that 27% is significantly below 50%.

  • You use CRITBINOM to test the null hypothesis: 60 trials with a proportion of 50% at the lower end's significance level (one-tail: 5%). In cell K4, you use =CRITBINOM(D4,I4,0.05).

  • Because 16 cases is below the 5% level of 24 cases (if random), the verdict is: significant. Cell L4 contains the formula: =IF(B4.

• In the second case, you test whether drinking caffeine increases the proportion of high systolic blood pressure:

  • You test the null hypothesis ( p=50%) at one tail: >95%.

  • In cell K9, you type =CRITBINOM(D9,I9,J9).

  • The verdict is: =IF(B9.

• In the third case, you test...