Question

an agricultural researcher wishes to see if a kelp extract prevents frost damage on tomato plants. two similar small plots are going to be planted with the same variety of tomato. plants in both plots are treated identically, expect the plants on plot 1 are going to be sprayed weekly with a kelp extract while the the plants in a plot 2 are not. let p1 and p2 be the actual proportion of all tomatoes of this variety that would experience crop damage under the kelp and no kelp treatments, respectively, when grown under conditions similar to those in the experiment. which of the following results would indicate that a difference exists between the two treatments? (a) the 95% confidence interval for p1-p2 is (-0.279, -0.035). (b) the 95% confidence interval for p1-p2 is (-0.279, 0.035) (c) the 95% confidence interval for p1-p2 is (0.0279, 0.350) (d) all of the above (e) only (a) and (c)

Answer 1

When we need to find if there is a statistical difference in proportions, the hypothesis we use is

H0: p1 - p2 = 0 vs Ha: p1 - p2   0.

When confidence intervals are used to see if there are statistical differences in proportions (or means) the lower limit and the upper limit should have the same sign, i.e both should either be negative or both should be positive. If one is negative and the other positive, it mean that the CI contains 0, and we would fail to reject H0.

Here we see that Option (a) has both its limits negative and option (c) has both its limits positive.

Therefore Option (e): Only (a) and (c).