Question

Bank employees from a large international bank were recruited with 67 assigned at

random to a control group and the remaining 61 assigned to a treatment group.

All subjects performed a coin-tossing task that required tossing any coin 10 times and reporting the results online. They were told they would win $20 for each head tossed for a maximum payoff of $200. Subjects were unobserved during the task, making it impossible to tell if a particular subject cheated. If the banking culture favors dishonest behavior, it was conjectured that it should be possible to trigger this behavior by reminding subjects of their profession (the “treatment”). Here are the results. The first line gives the possible number of heads on 10 tosses, and the next two lines give the number of subjects that reported tossing this number of heads for the control and treatment groups, respectively (for example, 16 control subjects reported getting four heads).

Number of Heads:    0, 1, 2, 3, 4, 5, 7, 8, 9, 10

Control Group :     0, 0, 1, 8, 16, 17, 14, 6, 2, 1, 2

Treatment Group:  0, 0, 2, 4, 8, 14, 15, 7, 6, 0, 5

If a subject is cheating, we would expect them to report doing better than chance, or tossing six or more heads.

1.  Find the proportion of subjects in each group that reported tossing six or more heads.

2. Test the hypotheses that the proportions reporting tossing six or more heads in the two groups are the same against the appropriate alternative. Explain your conclusions in the context of the problem, being sure to relate this to the researcher’s conjecture.

Answer 1

Answer:

Given that:

Bank employees from a large international bank were requited with 67 assigned at random toa control group and the remaining 61 assigned to a treatment group.

(a)

The proportion of subjects in the control group = 25/67

= 0.37

The proportion of subjects in the treatment group = 33/67

= 0.54

(b) The hypothesis being tested is:

H0: p1 = p2

Ha: p1 ≠ p2

p1	p2	Pc
0.373	0.541	0.4531	p(as decimal)
25/67	33/61	58/128	p(as fraction)
25.	33.	58.	X
67	61	128	n
	-0.1678	Difference
	0.	Hypothesized difference
	0.0881	std.error
	-1.91	z
	.0567	p-value (two tailed)

Since the p-value (0.0567) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we can conclude that the proportions reporting six or more heads in the two groups are the same.