In a study of the accuracy of fast food drive-through orders, Restaurant A had 302accurate orders and 59that were not accurate. a. Construct a 95%confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part (a) to this 95%confidence interval for the percentage of orders that are not accurate at Restaurant B: 0.143less thanpless than0.219.What do you conclude?

(a) A 95% confidence interval estimate of the percentage of orders that are not accurate is [0.125, 0.201].

(b) We can conclude that both restaurants can have the same inaccuracy rate due to the overlap of interval areas.

Step-by-step explanation:

We are given that in a study of the accuracy of fast food drive-through orders, Restaurant A had 302 accurate orders and 59 orders that were not accurate.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                          P.Q.  =    ~ N(0,1)

where, = sample proportion of orders that were not accurate = = 0.163

          n = sample of total orders = 302 + 59 = 361

          p = population proportion of orders that are not accurate

Here for constructing a 95% confidence interval we have used a One-sample z-test for proportions.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                    of significance are -1.96 & 1.96}  

P(-1.96 < < 1.96) = 0.95

P( < < ) = 0.95

P( < p < ) = 0.95

95% confidence interval for p = [ , ]

  = [ , ]

  = [0.125, 0.201]

(a) Therefore, a 95% confidence interval estimate of the percentage of orders that are not accurate is [0.125, 0.201].

(b) We are given that the 95% confidence interval for the percentage of orders that are not accurate at Restaurant B is [0.143 < p < 0.219].

Here we can observe that there is a common area of inaccurate order of 0.058 or 5.85% for both the restaurants.

So, we can conclude that both restaurants can have the same inaccuracy rate due to the overlap of interval areas.

1 is c

2 is a

3 is a

step-by-step explanation:

560

hope this : )