Question

drug sniffing dogs must be 95% accurate in their responses because their handlers don't want them to miss durgs and also don't want false positives. a new dog is being tested and is right in 46 of 50 trials. find the 95% confidence interval for the proportion of times the dog will be correct

Answer 1

Answer:

95% Confidence interval:  (0.8449,0.9951)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 50

Number of times the dog is right, x = 46

$\hat{p} = \dfrac{x}{n} = \dfrac{46}{50} = 0.92$

95% Confidence interval:

$\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting the values, we get:

$0.92 \pm 1.96(\sqrt{\dfrac{0.92(1-0.92)}{50}})\\\\ = 0.92\pm 0.0751\\\\=(0.8449,0.9951)$

(0.8449,0.9951) is the required 95% confidence interval for the proportion of times the dog will be correct.