Question

In 2010, the United Nations claimed that there was a higher rate of college graduates in men than in women from the country of A. A fact finding organization went to country A to conduct a random sample from a population of 10 million people The results revealed that 60 percent of 2500 men and 54 percent of 2510 women had college degrees. Do these results indicate that the United Nations findings were correct? (Assume significance level α=0.01) Be sure to verify the conditions.  

Test an appropriate hypothesis and state your conclusion.

Answer 1

Clearly it is proportion test ,

let,

Sample size for men = 2500 , let

Sample size for women = 2510 , let  

No. of mens having college degree from sample of 2500 men

No. of womens having college degree from sample of 2510 women

Proportion of mens having degree from sample of 2510 women

Proportion of mens having degree from sample of 2500 men

60% of 2500 = 1500

54% of 2510 = 1355.4

Hypothesis :

Test Statistic :

Where &

Table value

Take

Decision Rule :

if then we reject at 1% level of significance

here 4.2777>2.32

i.e

Decision : We can reject   at 1% level of significance

Conclusion :

United Nations findings were correct

i.e. there was a higher rate of college graduates in men than in women