6. In 2000, the United Nations claimed that there was a higher rate of illiteracy in men than in women from the country of Qatar. A humanitarian organization went to Qatar to conduct a random sample. The results revealed that 45 out of 234 men and 42 out of 251 women were classified as illiterate on the same measurement test. Do these results indicate that the United Nations findings were correct?

Question

6. In 2000, the United Nations claimed that there was a higher rate of illiteracy in men than in women from the country of Qatar.  A humanitarian organization went to Qatar to conduct a random sample.  The results revealed that 45 out of 234 men and 42 out of 251 women were classified as illiterate on the same measurement test.  Do these results indicate that the United Nations findings were correct?

drwls · Answer

For those samples, the rate is 19.2% for men and 16.7% for women. A higher rate for men is likley but no proven. You must also consider the sample size and standard deviation.

If the male illiteracy probability were 19%, the expected standard deviation in the number of illiterate men in a sample of 234 would be
sqrt(0.19*0.81*234) = 6.0, and for women in 251 cases it would be sqrt(0.17*0.83*251) = 6.0 also. This means the reported male illiteracy rate has a standard deviation of 2.6% and the female rate has a standard deviation of 2.4%. Think of these as the probabe errors in the measurement.

The separation of the two illiteracy rates is only about one standard deviation, so the findings do not have a high degree of statistical significance.