Question

To analyze how well lie detectors perform when subjects are stressed, 48 randomly chosen
subjects were connected to a lie detector and asked to read true statements out loud while
receiving an electric shock. The lie detector incorrectly reported that 27 of the 48 participants
were lying.
Note: For this problem, you will have to enter the counts directly into StatKey. Do not use
any of the book’s available datasets to answer the following questions!

(a) Use StatKey to determine the best estimate, based on this data, of the proportion of times
the lie detector yields false positives, i.e., inaccurately reports deception.
(b) Use StatKey to create 5000 bootstrap samples and a bootstrap distribution of sample
proportions. What are the center and standard error of your bootstrap distribution?
(c) Use StatKey and your bootstrap distribution to find a 95% confidence interval for the
overall percentage of false positives reported by the lie detector. What is the margin of
error?
(d) Does this sample provide evidence that lie detectors give inaccurate results more than half
the time when subjects are stressed? State the relevant null and alternative hypotheses,
use StatKey to create a randomization distribution based on this sample and H0, obtain
the p-value, and state your conclusion clearly.

Answer 1

(a) The best estimate of the proportion of times the lie detector yields false positives = 0.563

(b) The center is 0.5

The standard error is 0.072.

(c) The 95% confidence interval for the overall percentage of false positives reported by the lie detector is 0.3586 and 0.6414 with a margin of error of 0.1414.

(d) The hypothesis being tested is:

H₀: p = 0.5

H_a: p > 0.5

Observed	Hypothesized
0.5	0.5	p (as decimal)
24/48	24/48	p (as fraction)
24.	24.	X
48	48	n
	0.0722	std. error
	0.00	z
	.5000	p-value (one-tailed, upper)

The p-value is 0.5000.

Since the p-value (0.5000) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that lie detectors give inaccurate results more than half the time when subjects are stressed.

The Statkey output is:

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