According to New Scientist (January 2, 2012), a new thermal imaging camera that

Question

According to New Scientist (January 2, 2012), a new thermal imaging camera that detects small temperature changes is now being used as a polygraph device. The United State Department of Defense Polygraph Institute (DDPI) claims that the camera can detect liars correctly 75% of the time by monitoring the temperatures of their faces.

a. Set up the null and alternative hypotheses for testing the claim made by the DDPI. Be sure to dene the parameter used in your hypotheses.

b. Determine what type I and type II errors are for your hypothesis test.

c. Give two possible strategies in order to improve the power of this test?

d. If the level of signicance is prespecied to be 0.05, give the reject region of this test. Assume that sample size is large enough for this test.

Explanation / Answer

Solution:

a)      The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: The camera detects the liars correctly 75% of the time by monitoring the temperatures of their faces.

Alternative hypothesis: Ha: The camera does not detect the liars correctly 75% of the time by monitoring the temperatures of their faces.

Symbolically, the null and alternative hypothesis is given as below:

H0 P = 0.75 versus Ha: P 0.75

b)      The type I and type II error are given as below:

Type I error is the probability of rejecting the null hypothesis when actually camera detects the liars correctly 75% of the time by monitoring the temperatures of their faces.

Type II error is the probability of do not rejecting the null hypothesis when actually camera does not detect the liars correctly 75% of the time by monitoring the temperatures of their faces.

c)       For improving the power of the test, we need to increase the sample size and increase the confidence level.

d)      By assuming the large sample size we need to use the z-distribution or one sample z test for the population proportion. For this z test we are given the level of significance or alpha value as 0.05. The critical value for this test is given as Z = 1.645

Reject region is given as below:

Reject the null hypothesis if test statistic Z > Critical Z = 1.645

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.