Question

In a study of red/green color blindness, 700 men and 2850 women are randomly selected and tested. Among the men, 61 have red/green color blindness. Among the women, 7 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness. (Note: Type ‘‘p_m″ for the symbol pm , for example p_mnot=p_w for the proportions are not equal, p_m>p_w for the proportion of men with color blindness is larger, p_m)

(a) State the null hypothesis:

(b) State the alternative hypothesis:

Note that computation of the test statistic will produce z = 14.65

Answer 1

a)

H0: pm <= pw

b)

Ha: pm > pw

Sample proportion 1 = 61 / 700 = 0.0871

Sample proportion 2 = 7 / 2850 = 0.0025

Pooled proportion = (61 + 7) / (700 + 2850) = 0.0192

Test statistics

z = 1 - 2 / Sqrt [ ( 1 - ) * ( 1 / n1 + 1 \ n2) ]

= (0.0871 - 0.0025 / sqrt [ 0.0192 * 0.9808 * (1 / 700 + 1 / 2850) ]

= 14.65

Critical value at 0.05 level =.1.645

Since test statistics > 1.645 , reject the null hypothesis