Respuesta :
Answer:
There is a significant difference between the two proportions.
Step-by-step explanation:
The (1 - α)% confidence interval for difference between population proportions is:
[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]
Compute the sample proportions as follows:
[tex]\hat p_{1}=\frac{80}{250}=0.32\\\\\hat p_{2}=\frac{40}{175}=0.23[/tex]
The critical value of z for 90% confidence interval is:
[tex]z_{0.10/2}=z_{0.05}=1.645[/tex]
Compute a 90% confidence interval for the difference between the proportions of women in these two fields of engineering as follows:
[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]
[tex]=(0.32-0.23)\pm 1.645\times\sqrt{\frac{0.32(1-0.32)}{250}+\frac{0.23(1-0.23)}{175}}\\\\=0.09\pm 0.0714\\\\=(0.0186, 0.1614)\\\\\approx (0.02, 0.16)[/tex]
There will be no difference between the two proportions if the 90% confidence interval consists of 0.
But the 90% confidence interval does not consists of 0.
Thus, there is a significant difference between the two proportions.
