Question

Among a sample of 360 biology program applications, 198 of them are female applicants. (a) Find a 90% confidence interval of the true population proportion of female who applied to the biology program. (b) At a 0.05 significance level, test that the population proportion of female applicants is greater than 0.5 (Use critical value approach).

Answer 1

Solution-:

Let, X - Be the number of female applicants for biology program among 360 biology program

Given:

   So ,

(a) We find a 90% confidence interval of the true population proportion of female who applied to the biology program
is as follows;

  

(From Normal Probability Integral Table)

The required C.I. is

(b) At

Hypothesis: Vs  

Under the test statistic is given by,

Critical value-:  

(From Normal Probability Integral Table)

Decision Rule: Here, hence, we reject at 5 % level of significance.

Conclusion: We conclude that the population proportion of female applicants is greater than 0.5.