In order to assess the prevalence of color blindness in the

In order to assess the prevalence of color blindness in the state\'s male a public health agency selects a SRS of males and tests them for color blindness. In the sample of 400 men, 30 tested positive for color blindness. The agency would like to report an estimate for the true proportion of the state\'s male residents that are color blind.

1. Construct a 90% CI for the true proportion

2. What the margin of error?

3. How do you interpret your CI?

4. Another study claimed that the true proportion of the states male residents that are color blind is 0.12, test this claim with your confidence interval. Is it a reasonable claim? Why are why not?

5. For the given conditions of confidence level and margin of error, find the sample size required to meet those condition and fill in the appropriate cells in the table below:

6. As the confidence level increases, while ME stays the same, does the required sample size increase, decrease, or stay the same?

7. As the ME decreases, while confidence level stays the same, does the required sample size increase, decrease, or stays the same?

Solution

1.

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.075          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.013169567          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    2.33          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.044314908          
upper bound = p^ + z(alpha/2) * sp =    0.105685092          
              
Thus, the confidence interval is              
              
(   0.044314908   ,   0.105685092   ) [ANSWER]

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2.

Margin of error = (upper - lower)/2 = 0.030685092 [answer]

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3.

We are 90% confident that the true population proportion is between 0.044314908 and 0.105685092.

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4.

It is not a reasonable claim at 0.10 significance, as our confidence interval does not include 0.12.

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