Example of a proportional confidence interval formula:
CI99 = p + or - (2.58)[√(pq/n)]
...where p = x/n, q = 1 - p, and n = sample size.
Note: + or - 2.58 represents 99% confidence interval.
You will need to find the z-value for the 90% interval in the problem.
For p in your problem: 16/50 = .32
For q: 1 - p = 1 - .32 = 68
n = 50
I let you take it from here.
A company claims to have invented a hand-held sensor that can detect the presence of explosives
inside a closed container. Law enforcement and security agencies are very interested in purchasing several of the devices if they are shown to perform effectively. An independent laboratory arranged a test. They placed four empty boxes in the corners of an otherwise empty room. For each trial they put a small quantity of an explosive in one of the boxes selected at random. The company’s technician then entered the room and used the sensor to try to determine which of the four boxes contained the explosive. The experiment consisted of 50 trials, and the technician was successful in finding the explosive 16 times. Does this indicate that the device is effective in sensing the presence of explosives? Test an appropriate hypothesis and state your conclusion. Find and interpret a 90% confidence interval.
2 answers
Correction: q = .68
2 answers