Question

• An alien empire is considering taking over planet Earth, but they will only do so if the portion of rebellious humans is less than 10%. They abducted a random sample of 400 humans, performed special psychological tests, and found that 12% of the sample are rebellious.
• Let's test the null hypothesis that the actual percentage of rebellious humans is 10% versus the alternative that the actual percentage is higher than that.
• The table at right sums up the results of 1000 simulations, each simulating a sample of 400 humans, assuming there are 10%, percent rebellious humans.
• According to the simulations, what is the probability of getting a sample with 10% rebellious humans or less?
• Let's agree that if the observed outcome has a probability less than 1% under the tested hypothesis, we will reject the hypothesis.
• What should we conclude regarding the hypothesis?
  • We cannot reject the null hypothesis.
  • We should reject the null hypothesis.

Measured % of rebellious humans	Frequency
6	7
7	40
8	93
9	173
10	327
11	253
12	73
13	27
14	7

Answer 1

According to the simulations, what is the probability of getting a sample with 10% rebellious humans or less?

640/1000 = 0.64

• What should we conclude regarding the hypothesis?
  • We cannot reject the null hypothesis.
  • We should reject the null hypothesis.

Observed	Hypothesized
0.64	0.1	p (as decimal)
640/1000	100/1000	p (as fraction)
640.	100.	X
1000	1000	n
	0.0095	std. error
	56.92	z
	0.00E+00	p-value (one-tailed, upper)