Question

In a study of color perception, 356 men are tested, and 39 are found to have red/green color blindness.

1. n ˆ p ( 1 − ˆ p ) =

2. ˆ p =

3. Is n ˆ p ( 1 − ˆ p ) ≥ 10 ?( yes or no)

4. The margin of error is use the 85 % confidence level

5.Construct a 85 % confidence interval for the percent of men in general population who are color blind. Lower Bound Upper Bound

Answer 1

Total number of men tested = n = 356

Number of men who have red/green color blindness = x = 39

Sample proportion = = x/n = 39/356 = 0.10955

1)

2)

Sample proportion = = 39/356 = 0.10955

4)

Margin of Error ( E ) :

Where , is critical value for given confidence level.

Confidence level = 85% = 0.85

Significance level = = 1 - 0.85 = 0.15 , /2 = 0.15/2 = 0.075

= = 1.4395    { using Excel function ,  =NORMSINV(1-0.075) =1.4395 }

So margin of error is ,

5)

The 85 % confidence interval for the percent of men in general population who are color blind is ,

Lower bound =   - E = 0.10955 - 0.02383 =0.08572

Upper bound =   + E =  0.10955 +0.02383 = 0.13338