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?

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.

To determine whether the results gathered by the humanitarian organization in Qatar support the United Nations' claim of higher illiteracy rate in men than in women, we can perform a hypothesis test.

Let's define our hypotheses:
- Null hypothesis (H₀): The illiteracy rates among men and women in Qatar are equal.
- Alternate hypothesis (H₁): The illiteracy rates among men and women in Qatar are not equal.

Next, we need to calculate the test statistic and p-value to make a conclusion. We can use the chi-square test for this analysis.

Step 1: Calculate the expected values for each category assuming equal illiteracy rates in men and women.
- Expected value for illiterate men = (total men / total population) * (total illiterate)
- Expected value for illiterate women = (total women / total population) * (total illiterate)

Step 2: Calculate the chi-square test statistic.
- Chi-square statistic = Σ [(observed - expected)² / expected]

Step 3: Determine the degrees of freedom (df).
- df = (# of rows - 1) * (# of columns - 1)

Step 4: Determine the p-value using the chi-square distribution with the calculated chi-square statistic and degrees of freedom.

Step 5: Compare the calculated p-value with a pre-determined significance level (usually 0.05) to make a conclusion. If the p-value is less than the significance level, we reject the null hypothesis and conclude that the illiteracy rates are different. If the p-value is greater than the significance level, we fail to reject the null hypothesis.

By following these steps and performing the calculations based on the provided data, you can determine whether the results from the sample in Qatar support the United Nations' claim.