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1. In a study of red/green color blindness, 1000 men and 2650 women are randomly selected and tested. Among the men, 90 have red/green color blindness. Among the women, 7 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness. The test statistic is The p-value is Is there sufficient evidence to support the claim that men have a higher rate of red/green color blindness than women using the 0.01% significance level?

A)Yes
B)No

User Taveced
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Final answer:

The rate of red/green color blindness is higher in men than in women according to the sample data. If the p-value is less than the significance level, the null hypothesis is rejected, confirming that men have a higher rate. Without the actual p-value in the question, a hypothetical situation validates the claim with a p-value of 0.005 against a 0.01% significance level.

Step-by-step explanation:

In testing the claim that men have a higher rate of red/green color blindness than women, we can use the numbers provided to calculate the rates of color blindness in both genders and conduct a hypothesis test to determine if there is a significant difference. The rate for men is 90/1000, or 9%, and the rate for women is 7/2650, which is approximately 0.26%. To test this claim, we set up the null hypothesis (H0) that the rates are equal and the alternative hypothesis (H1) that the rate for men is higher than that for women.

Given the p-value of a study is essential for decision making. The p-value represents the probability of observing a result as extreme as the one measured in the study, or more extreme if the null hypothesis were true. If the p-value is less than the alpha level of significance, we reject the null hypothesis.

The problem statement does not provide an actual p-value, but to illustrate, let's say our study returned a p-value of 0.005, which is less than both the conventional alpha levels of 0.05 and the more stringent 0.01% (0.0001) significance level mentioned in the question. Consequently, we would reject the null hypothesis and conclude there is sufficient evidence to support the claim that men have a higher rate of red/green colour blindness than women.

User Matt Sephton
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