Question

A new disease has annihilating amphibian populations at unprecedented levels. Researchers has been trying to develop some treatment that can counteract the disease and save some of the amphibian populations. To test which of two potential solutions is more effective, they take a sample of frogs and randomly divide them into two groups. After being treated, 256 of the 400 frogs in group 1 ended up surviving exposure to the pathogen; 300 of the 482 frogs in the second group survived. For the following questions, calculate your difference in the order: group 1 - group 2. The standard error of the difference was 0.033.

(a) What are the hypotheses they should test to see if the treatments given to the two groups have different effectiveness? H₀:  --- μ1-μ2 = 0 μd = 0 p1-p2 = 0 vs. H_a:  --- p1-p2 > 0 μd ≠ 0 μ1-μ2 ≠ 0 p1-p2 ≠ 0

(b) Calculate the test statistic:

(c) Find the p-value:

(d) What could we conclude from the test?

Neither treatment was significantly more effective than the other.The treatment given to group 1 was not more effective.    The treatment given to group 2 was more effective.The treatment given to group 1 was more effective.The treatment given to group 2 was not more effective.

Answer 1

a)

H0: p1-p2 = 0 vs. Ha: p1-p2 > 0

b)

p1cap = X1/N1 = 256/400 = 0.64
p1cap = X2/N2 = 300/482 = 0.6224

z = ( p1 -p2)/SE
= (0.64 - 0.6224)/0.033
= 0.53

c)

p value = 0.5961

d)

Neither treatment was significantly more effective than the other.