Question

In a group of 227 taking an experimental pill, 52 developed nausea. In a group of 45 taking a placebo, 5 developed nausea. Find the test statistic to test the claim that the proportion of all taking the experiment pill developing nausea is greater than the proportion of all taking the placebo developing nausea. Use a 0.05 significance level.

Answer 1

The hypothesis being tested is:

H₀: p₁ = p₂

H_a: p₁ > p₂

p1	p2	pc
0.2291	0.1111	0.2096	p (as decimal)
52/227	5/45	57/272	p (as fraction)
52.	5.	57.	X
227	45	272	n
	0.118	difference
	0.	hypothesized difference
	0.0664	std. error
	1.78	z
	.0378	p-value (one-tailed, upper)

The test statistic is 1.78.

The p-value is 0.0378.

Since the p-value (0.0378) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the proportion of all taking the experiment pill developing nausea is greater than the proportion of all taking the placebo developing nausea.