Answer to Question #182738 in Statistics and Probability for Nicole Andrea Plid

Question

From year to year, It has been observed that there is a greater number of women who are graduating from college, RAPA university noted that in 2015, 40% of their college graduates were women. Supposed a random sample of 120 graduating college students this year were selected. Of this number 57 were women. That this indicate that the proportion of college graduates that are women this year is significantly higher than the proportion in 2015? Use the rejection region approach using 0.10 level of significance

Answer 1

Let $H_o:$ The proportion of women is higher in this year as compared to 2015

and $H_a:$ The proportion of women is not higher in this year as compared to 2015

$p=0.4 \\ n=120 \\ \hat{p}=\dfrac{57}{120}=0.475$

$\alpha=0.1$

Test-statistics-

$z=\dfrac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$

$=\dfrac{(0.475-0.4)\sqrt{120}}{\sqrt{0.4(1-0.4)}}\\[9pt]=\dfrac{0.075\times 10.95}{\sqrt{0.24}}\\[9pt]=1.67$

$P(z>1.67)=0.04668$

Conclusion: As calculated p-vaue is less than $\alpha$ i.e. 0.10 So we reject Null hypothesis. i.e. There are not enough evidence to support the claim tha proportion of women higher in this year as compared to 2015.