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, 257 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: vs. Ha: (b) Calculate the test statistic: (c) Find the p-value: (d) What could we conclude from the test?

Answer 1

(A) Researcher want to test if there is any difference between the two groups or not

Null hypothesis:-

Alternate hypothesis

(B) test statistics z =

where p1(hat) = 257/400 and p2(hat) = 300/482 and SE = 0.033

this implies

= [(257/400)-(300/482)]/0.033

= 0.02009/0.033

= 0.61

(C) using z distribution table for two tailed hypothesis, checking 0.6 in the first left column and 0.01 in the first row, then selecting the intersecting cell

this implies

p value = 0.5419

(D) p value is greater than 0.05 as well as 0.10 level of significance, which means that the result is insignificant. Therefore, we are failing to reject the null hypothesis.

We can conclude that there is no significant difference between the two groups