Answer :
Answer:
(a) The 90% confidence interval estimate of the percentage of orders that are not accurate in Restaurant A is (0.148, 0.222).
(b) Restaurant B has more proportion of not accurate orders.
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(1-\hat p)}{n}}[/tex]
(a)
In Restaurant A the number of not accurate orders was x = 55 of n = 297 orders.
The sample proportion of not accurate orders in Restaurant A is:
[tex]\hat p=\frac{x}{n}=\frac{55}{297}=0.1852[/tex]
The critical value of z for 90% confidence level is:
[tex]z_{\alpha/2}=z_{0.10/2}=z_{0.05}=1.645[/tex]
Compute the 90% confidence interval estimate of the percentage of orders that are not accurate in Restaurant A as follows:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.1852\pm 1.645\sqrt{\frac{0.1852(1-0.1852)}{297}}\\=0.1852\pm 0.0371\\=(0.1481, 0.2223)\\\approx (0.148, 0.222)[/tex]
Thus, the 90% confidence interval estimate of the percentage of orders that are not accurate in Restaurant A is (0.148, 0.222).
(b)
The 90% confidence interval estimate of the percentage of orders that are not accurate in Restaurant B is (0.171, 0.245).
The confidence interval for Restaurant B indicates that between 17.1% to 24.5% orders are inaccurate.
The values of this interval is more than that for Restaurant A.
So, it can be concluded that Restaurant B has more proportion of not accurate orders.