Question

For the color blindness data in Exercise 16.HE.A, we wish to test a hypothesis to answer the question, “Has the instance of color blindness increased from the historical rate of 1%?”

"16.HE.A: It is estimated that 1% of the population suffers from red/green color blindness (Source: USA Today). The ophthalmology department of a large university medical center randomly tests 300 men. 11 are found to have this type of color blindness.

(a)      Check the necessary assumptions and conditions for a confidence interval.

1. Independence? Random tests= Yes
2. 10% Condition? Less than 10% of population = Yes, 1%
3. Success less than 10 and Failure less than 10 expected = Yes (barely though with 11 color blindness)

(b)      Compute a 95% confidence interval estimate of the proportion of all men with this type of color blindness.

          1.54% and 5.79%

(c)      State your conclusion in context.

          I am 95% confident that between 1.54% and 5.79% of the proportion of all men have red/green color blindness.

(d)      What sample size would be needed to estimate the proportion of male red / green color blindness if we wanted 96% confidence that the margin of error is no more than 3%, assuming the data from the exercise?

          N = 165

(e)      If we make the (very unrealistic) assumption that half of the 300 were colorblind, what sample size should we then need for subsequent studies if we want no more than a 3% margin of error.

Solve 0.03 = 2.0537*sqrt(0.5*0.5/x).. = 1171.57 = 1172"

1. Write appropriate hypotheses.

                    

         

2. Check the necessary assumptions and conditions for the test, given that we completed Exercise 16.HE.A.

3. Perform the test. What is the p-value?

4. Explain carefully what the p-value means in this context.

5. What is your conclusion? (Use alpha-level 0.05.)

Answer 1

(b)

Since so  the necessary assumptions and conditions for the test did not meet.

(d)

The p-value gives the probability of getting sample results or more extreme results under the assumption that null hypothesis is true.