A certain geneticist is interested in the proportion of males and females in the population that have a certain minor blood disorder. In a random sample of 1500 males, 75 are found to have disorder, whereas 80 of 2000 females appear to have disorder. Find a 90% confidence intervals for the difference between the proportions of males and females that have blood disorder. Also test the hypotheses claims that the proportion of males who have blood disorder is more than the proportion of females at the 0.1 level of significance.

To find the confidence interval for the difference between the proportions of males and females with the blood disorder, we can use the formula for the confidence interval for the difference between two proportions:

Confidence interval = (p₁ - p₂) ± z * sqrt((p₁ * (1 - p₁) / n₁) + (p₂ * (1 - p₂) / n₂))

where:
- p₁ and p₂ are the proportions of males and females with the blood disorder, respectively
- n₁ and n₂ are the sample sizes of males and females, respectively
- z is the z-score corresponding to the desired confidence level

To test the hypothesis that the proportion of males with the blood disorder is greater than the proportion of females, we can perform a hypothesis test using the following steps:

Step 1: State the null and alternative hypotheses:
- Null hypothesis (H₀): p₁ <= p₂
- Alternative hypothesis (H₁): p₁ > p₂

Step 2: Set the significance level (α). In this case, α = 0.1.

Step 3: Compute the test statistic:
- For this hypothesis test, we can use the z-test for comparing two proportions. The test statistic is given by:

test statistic = (p₁ - p₂) / sqrt((p₁ * (1 - p₁) / n₁) + (p₂ * (1 - p₂) / n₂))

Step 4: Find the critical value:
- The critical value is the z-score corresponding to the desired significance level (α = 0.1) in the right tail of the standard normal distribution.

Step 5: Compare the test statistic to the critical value:
- If the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Now let's calculate the confidence interval and perform the hypothesis test:

First, calculate the proportions:
p₁ = 75 / 1500 = 0.05
p₂ = 80 / 2000 = 0.04

Next, calculate the standard errors:
standard error₁ = sqrt((p₁ * (1 - p₁) / n₁)) = sqrt((0.05 * 0.95) / 1500)
standard error₂ = sqrt((p₂ * (1 - p₂) / n₂)) = sqrt((0.04 * 0.96) / 2000)

Now, calculate the confidence interval using the formula:
Confidence interval = (p₁ - p₂) ± z * sqrt((p₁ * (1 - p₁) / n₁) + (p₂ * (1 - p₂) / n₂))

Substituting the values, assuming a 90% confidence level (z = 1.645):
Confidence interval = (0.05 - 0.04) ± 1.645 * sqrt((0.05 * 0.95 / 1500) + (0.04 * 0.96 / 2000))

Finally, perform the hypothesis test:
Compute the test statistic using the formula:
test statistic = (p₁ - p₂) / sqrt((p₁ * (1 - p₁) / n₁) + (p₂ * (1 - p₂) / n₂))

Compare the test statistic to the critical value (z = z-score for α = 0.1).

If the test statistic > critical value, reject the null hypothesis (H₀); otherwise, fail to reject the null hypothesis.

These steps should help you find the 90% confidence interval for the difference between the proportions of males and females with the blood disorder and perform the hypothesis test.