Respuesta :
Answer:
The value of α is 0.10.
Step-by-step explanation:
The (1 - α)% confidence interval for population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p\times\hat q}{n}}[/tex] OR [tex]CI=\hat p\pm E[/tex]
The information provided is:
n = 500
[tex]\hat p[/tex] = 0.11
E = ± 0.05
In the (1 - α)% confidence interval for population proportion the variables are defined as follows:
[tex]\hat p[/tex] = sample proportion of people who chose chocolate pie
[tex]\hat q[/tex] = sample proportion of people who did not choose chocolate pie
n = sample selected for the poll
E = margin of error for the (1 - α)% confidence interval
p = population proportion of people who chose chocolate pie
The confidence level used is, 99%.
Compute the value of α as follows:
[tex](1-\alpha )\%=99\%\\100\%-\alpha \%=99\%\\\alpha \%=100\%-99\%\\\alpha \%=10\%\\\alpha =0.10[/tex]
Thus, the value of α is 0.10.
