SOLUTION: 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

Question 276388: 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?
1. Test an appropriate hypothesis and state your conclusion.
2. Was your test one-tail lower, or two tail? Explain why you chose that kind of test in this situation.
3. Explain what your P-value means in this context.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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?
1. Test an appropriate hypothesis and state your conclusion.
Ho: p >= 0.5
Ha: p < 0.5
-------------
2. Was your test one-tail lower, or two tail? Explain why you chose that kind of test in this situation.
--
One-tail lower because we are assuming a detection level higher than random.
We do not want to have a rejection interval where p-hat is a high number,
only where p-hat is a lower number.
--------------------------------------------

3. Explain what your P-value means in this context.
The p-value will be the probability that test results could give
stronger evidence for rejecting Ho.
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Cheers,
Stan H.

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