Question

New ultra-sound2 device designed to detect the presence of a metallic-object in a wooden enclosure is used for a pilot test. During trial, 281 wooden enclosures were truly embedded with marked metallic-object. The other 252 wooden enclosures were intentionally NOT enclosures with any metallic-object.

As the pilot test runs were conducted, the ultra-sound2 device detected 102 positive wooden enclosures truly embedded metallic-object out of the 281 wooden subjects truly embedded with metallic-object. Also, out of the other 252 (control) wooden enclosures NOT embedded with metallic-object the ultra-sound2 device did NOT pick up any metallic-object but showed negative in 172 runs.

1. After showing your table, step by step, construct a 90% confidence interval for the ultra-sound2 device selectivity.
2. Also, construct a 95% confidence interval for the ultra-sound2 device, sensitivity

Answer 1

(i) The 90% confidence interval for the ultra-sound2 device selectivity is between -0.387 and -0.2521.

p1	p2	pc
0.363	0.6825	0.5141	p (as decimal)
102/281	172/252	274/533	p (as fraction)
102.	172.	274.	X
281	252	533	n
	-0.3196	difference
	0.	hypothesized difference
	0.0434	std. error
	-0.387	confidence interval 90.% lower
	-0.2521	confidence interval 90.% upper
	0.0675	margin of error

(ii) The 95% confidence interval for the ultra-sound2 device selectivity is between -0.3999 and -0.2392.

p1	p2	pc
0.363	0.6825	0.5141	p (as decimal)
102/281	172/252	274/533	p (as fraction)
102.	172.	274.	X
281	252	533	n
	-0.3196	difference
	0.	hypothesized difference
	0.0434	std. error
	-0.3999	confidence interval 95.% lower
	-0.2392	confidence interval 95.% upper
	0.0804	margin of error