Question

The current method for 100% detection of contraband passing through X-Ray screeners by TSA agents in the United States is 14%. We develop a new way that teaches screeners to use different color schemes to illuminate items such that a person can see the items in the color scheme that makes sense to them. Out of the 24 TSA agents that volunteers to participate in a program, 8 were now capable of 100% detection. Perform an appropriate hypothesis test to determine if this is significantly different than the prior estimate.

Answer 1

Let p be the proportion of TSA agents capable of 100% detection. Then,

Null hypothesis H0: p = 0.14

Alternative hypothesis Ha: p 0.14

Let us assume the significance level = 0.05. We will use z test for one sample proportion.

Standard error of proportion, se =

= 0.0708

Sample proportion = = 8 / 24 = 0.3333

Test statistic, z = ( - p) / se =   (0.3333 - 0.14) / 0.0708 = 2.73

P(z > 2.73) = 0.0032

For two-tail test, p-value = 2 * 0.0032 = 0.0064

Since p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is significant evidence that the proportion of TSA agents capable of 100% detection is significantly different from the prior estimate (p 0.14)