Question

8. Nine of the 50 drivers pulled over on the weekend for speeding were also found to be DWI. During the week, four of the 30 drivers pulled over for speeding were DWI. Use a confidence interval to evaluate whether there is no difference between the rate of drunk driving on the weekend and during the week. (a.- 01) Confidence Interval Interpretation und n average of 17 (sd 2) on

Answer 1

(a)

n1 = 50

p1 = 9/50 = 0.18

n2 = 30

p2 = 4/30 =0.1333

$=\frac{9+4}{50+30}=0.1625$

Q = 1 - P = 0.8375

$SE=\sqrt{PQ(1/n1+1/n2)}$

$=\sqrt{0.1625\times 0.8375(1/50 + 1/30)}=0.0852$

$\alpha$ = 0.01

From Table, critical values of Z = $\pm$ 2.576

Confidence Interval:

(0.18 - 0.1333) $\pm$ (2.576 X 0.0852)

= 0.0467 $\pm$    0.2195

= ( - 0.1728, 0.2662)

(b) Interpretation:

If repeated samples are taken and the 99% Confidence Interval is computed for each sample, 99% of the intervals will contain the population difference between the rate of drunk driving on the weekend and during the week.