Respuesta :
Answer:
The upper bound for a 95% confidence interval for the true proportion of students at this university whose favorite dessert is affogato is 38%.
Step-by-step explanation:
The (1 - α) % confidence interval for population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
Compute the sample proportion as follows:
[tex]\hat p=\frac{43}{145}=0.2966\approx 0.30[/tex]
The critical value of z for 95% confidence level is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
Calculate the upper bound for a 95% confidence interval for the true proportion of students at this university whose favorite dessert is affogato as follows:
[tex]UL=\hat p+ z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]=0.30+1.96\times\sqrt{\frac{0.30(1-0.30)}{145}}\\\\=0.30+0.075\\\\=0.375\\\\\approx 0.38[/tex]
Thus, the upper bound for a 95% confidence interval for the true proportion of students at this university whose favorite dessert is affogato is 38%.
