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Leviafan [203]
4 years ago
9

(1 pt) In a study of red/green color blindness, 950 men and 2050 women are randomly selected and tested. Among the men, 89 have

red/green color blindness. Among the women, 6 have red/green color blindness. Construct the 99% confidence interval for the difference between the color blindness rates of men and women.
Mathematics
1 answer:
Ivahew [28]4 years ago
4 0

Answer: (0.066,0.116)

Step-by-step explanation:

The confidence interval for proportion is given by :-

p_1-p_2\pm z_{\alpha/2}\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}

Given : The proportion of men have red/green color blindness = p_1=\dfrac{89}{950}\approx0.094

The proportion of women have red/green color blindness = p_2=\dfrac{6}{2050}\approx0.003

Significance level : \alpha=1-0.99=0.01

Critical value : z_{\alpha/2}=z_{0.005}=\pm2.576

Now, the 99% confidence interval for the difference between the color blindness rates of men and women will be:-

(0.094-0.003)\pm (2.576)\sqrt{\dfrac{0.094(1-0.094)}{950}+\dfrac{0.003(1-0.003)}{2050}}\approx0.091\pm 0.025\\\\=(0.09-0.025,0.09+0.025)=(0.066,\ 0.116)

Hence, the 99% confidence interval for the difference between the color blindness rates of men and women= (0.066,0.116)

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