In a study of red/green color blindness. 1000 men and 2800 women are randomly selected and tested Among the men. 85 have red/green color blindness. Among the women, 6 have red/green color blindness.1. 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 0.05% significance level?A. Yes. B. No.2. Construct the 95% confidence interval for the difference between the color blindness rates of men and women <(P1âP2)<

1. Yes, there is sufficient evidence to support the claim that men have a higher rate of red/green color blindness than women.

2. The 95% confidence interval for the difference between the color blindness rates of men and women is [0.0656, 0.1004].

Step-by-step explanation:

We are given that in a study of red/green color blindness. 1000 men and 2800 women are randomly selected and tested

Among the men, 85 have red/green color blindness. Among the women, 6 have red/green color blindness.

Let = population proportion of men having red/green color blindness.

  = population proportion of women having red/green color blindness.

So, Null Hypothesis, :      {means that men have a lesser or equal rate of red/green color blindness than women}

Alternate Hypothesis, :      {means that men have a higher rate of red/green color blindness than women}

(1) The test statistics that will be used here is Two-sample z-test statistics for proportions;

                             T.S.  =     ~  

N(0,1)

where, = sample proportion of men having red/green color blindness = = 0.085

= sample proportion of women having red/green color blindness = = 0.002

= sample of men = 1000

= sample of women = 2800

So, the test statistics =    

                                     =  9.37    

The value of z-test statistics is 9.37.

Also, the P-value of the test statistics is given by;

               P-value = P(Z > 9.37) = Less than 0.0001

Since the P-value of our test statistics is less than the level of significance as 0.0001 < 0.05%, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we support the claim that men have a higher rate of red/green color blindness than women.

(2) The 95% confidence interval for the difference between the color blindness rates of men and women () is given by;

95% C.I. for () =

                                 =

                                 =

                                 = [0.0656, 0.1004]

Here, the crtical value of z at 2.5% level of significance is 1.96.

Hence, the 95% confidence interval for the difference between the color blindness rates of men and women is [0.0656, 0.1004].

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