Answer:
(a) The 90% confidence interval estimate of the percentage of orders that are not accurate in Restaurant <em>A</em> is (0.148, 0.222).
(b) Restaurant <em>B </em>has more proportion of not accurate orders.
Step-by-step explanation:
The (1 - <em>α</em>)% confidence interval for population proportion is:
(a)
In Restaurant <em>A</em> the number of not accurate orders was <em>x</em> = 55 of <em>n</em> = 297 orders.
The sample proportion of not accurate orders in Restaurant <em>A</em> is:
The critical value of <em>z</em> for 90% confidence level is:
Compute the 90% confidence interval estimate of the percentage of orders that are not accurate in Restaurant <em>A</em> as follows:
Thus, the 90% confidence interval estimate of the percentage of orders that are not accurate in Restaurant <em>A</em> is (0.148, 0.222).
(b)
The 90% confidence interval estimate of the percentage of orders that are not accurate in Restaurant <em>B</em> is (0.171, 0.245).
The confidence interval for Restaurant <em>B</em> indicates that between 17.1% to 24.5% orders are inaccurate.
The values of this interval is more than that for Restaurant <em>A</em>.
So, it can be concluded that Restaurant <em>B </em>has more proportion of not accurate orders.