Part A
p = population proportion of inaccurate orders for restaurant A.
There are 240 accurate orders and 73 inaccurate ones.
That gives 240+73 = 313 total orders.
n = 313 = sample size
73/313 = 0.233227 is the approximate sample proportion of inaccurate orders. This is the approximate value of phat. The job of phat is to estimate p.
At 90% confidence, the z critical value is roughly z = 1.645; use a stats table, reference sheet, or calculator to find this value.
Let's calculate the margin of error.
E = margin of error
E = z*sqrt(phat*(1-phat)/n)
E = 1.645*sqrt(0.233227*(1-0.233227)/313)
E = 0.039320 approximately
Then,
L = lower boundary of confidence interval
L = phat - E
L = 0.233227 - 0.039320
L = 0.193907
L = 0.194
And
U = upper boundary of confidence interval
U = phat + E
U = 0.233227 + 0.039320
U = 0.272547
U = 0.273
The 90% confidence interval for the inaccurate order rate of restaurant A is therefore 0.194 < p < 0.273
We are 90% confident the population proportion p is somewhere between 0.194 and 0.273
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Part B
The result of part A was 0.194 < p < 0.273
Compare this to 0.211 < p < 0.292 for restaurant B.
Use a number line to see that there is overlap between these intervals. It's possible that both restaurants might have the same inaccurate order rates (or close to the same).
If there wasn't an overlap, then it would be likely the two rates would be different.