Question

Specially trained dogs are used to detect explosives in the border control. In a random testing of 100 items, trained dogs detected trace of explosives in 4 of them. a) Find the standard deviation and the standard error estimate for the proportion of detected trace for explosives. * ANSWER USING EXCEL FUNCTIONS *   

b) Find the 95% confidence interval for the population proportion of detected trace for explosives. * ANSWER USING EXCEL FUNCTIONS *

c) Find the 90% confidence interval for the population proportion of detected trace for explosives. * ANSWER USING EXCEL FUNCTIONS *

- Thank you in advance

Answer 1

Proportion P	=4/100	0.04
Standard deviation	=SQRT(0.04*0.96)	0.195959
Standard error	=SQRT(0.04*0.96/100)	0.019596
Margin of error	=1.96 * SQRT(0.04*0.96/100)	0.038408
95% CI	=(P-ME , P+ME)	0.001592	0.078408
Margin of error	=1.645 * SQRT(0.04*0.96/100)	0.032235
90% CI	= (P-ME , P+ME)	0.007765	0.072235

a.

Standard deviation :

Vp (1-P) = 0.195959

Stnadard error

$\sqrt{\frac{\hat{p} \: (1-\hat{p})}{n}} =0.0195959$

b.

95% confidence interval is (0.001592, 0.078408)

c.

90% confidence interval is ( 0.007765 , 0.072235 )