Question

Problem 2 (20 pts). Hypothesis testing - Imagine a study designed to test whether daughters resemble their fathers. In each trial of the study, a participant examines a photo of one girl and photos of two adult men, one of whom is girl's father. The participant must guess is the father. If there is no daughter-father resemblance, then the probability that the participant guesses correctly is only 1/2. Possible-meaningful hypotheses are: Ho: Participants pick the father correctly half the time HA: Participants pick the father correctly more frequently than half the time. (a) Assume that 13 out of 18 participants correctly guessed the father of the daughter. Test the null hypothesis Ho. Calculate the P-value and compare it with the standard significance level (a = 0.05). Will you reject Ho? (b) Assume that 12 out of 18 were correct. Will you reject Ho? (C) Assume that 12 x 2 = 24 out of 18 x 2 = 36 were correct. Will you reject Ho? (d) How/why are your answers in (b) and (c) different? Caution: Examine carefully if this is a one-sided or two-sided test.

Answer 1

This is a one-sided test.

(a) The hypothesis being tested is:

H_o: Participants pick the father correctly half the time

H_A: Participants pick the father correctly more frequently than half the time.

The output is:

Observed	Hypothesized
0.7222	0.5	p (as decimal)
13/18	9/18	p (as fraction)
13.	9.	X
18	18	n
	0.1179	std. error
	1.89	z
	.0297	p-value (one-tailed, upper)

Since the p-value (0.0297) is less than the significance level, we can reject H_o.

(b) The hypothesis being tested is:

H_o: Participants pick the father correctly half the time

H_A: Participants pick the father correctly more frequently than half the time.

The output is:

Observed	Hypothesized
0.6667	0.5	p (as decimal)
12/18	9/18	p (as fraction)
12.	9.	X
18	18	n
	0.1179	std. error
	1.41	z
	.0786	p-value (one-tailed, upper)

Since the p-value (0.0786) is greater than the significance level, we cannot reject H_o.

(c) The hypothesis being tested is:

H_o: Participants pick the father correctly half the time

H_A: Participants pick the father correctly more frequently than half the time.

The output is:

Observed	Hypothesized
0.6667	0.5	p (as decimal)
24/36	18/36	p (as fraction)
24.	18.	X
36	36	n
	0.0833	std. error
	2.00	z
	.0228	p-value (one-tailed, upper)

Since the p-value (0.0228) is less than the significance level, we can reject H_o.

(d) The answers in (b) and (c) are different because we obtained a different p-value.