Question

8% of men are red-green colorblind. A sample of 125 men is gathered from a particular subpopulation, and 13 men in this sample are colorblind.

a. Is this statistically significant evidence that the proportion of red-green colorblind men is greater than the subpopulation than the national average with alpha = 0.05?

b. What is the maximum number of men that could have been colorblind in this sample that would lead you to fail to reject the null hypothesis?

c. Using 8% as the probability of being colorblind, find a 95% confidence interval for the number of men in a sample of 125 who are colorblind.

Answer 1

Claim:  the proportion of red-green colorblind men is greater than the subpopulation than the national average.

The null and alternative hypothesis is

H0: P 0.08

H1: P > 0.08

Level of significance = 0.05

Sample size = n = 125

x = 13

Test statistic is

Critical value = 1.64 ( Using z table)

Critical value > z we fail to reject the null hypothesis.

Conclusion:

There is not sufficient evidence that the proportion of red-green colorblind men is greater than the subpopulation than the national average with alpha = 0.05

b)The maximum number of men that could have been colorblind in this sample that would lead us to fail to reject the null hypothesis is

The rejection region for this right-tailed test is

So 125*0.1197=14.97

So if the number of people having colorblindness was 15 we would have rejected the null hypothesis. The maximum number is 14, that could have been colorblind in this sample that would lead us to fail to reject the null hypothesis.

c)

x= 13
n=125
p0=0.08

p=x/n
alpha=0.95

(0.05,0.158)