Answer:
Step-by-step explanation:
This is a test of 2 population proportions. Let 1 and 2 be the subscript for the the vines infested using Pernod 5 and vines infested using Action. The population proportion of the vines infested using Pernod 5 and vines infested using Action would be p1 and p2 respectively.
p1 - p2 = difference in the proportion of the vines infested using Pernod 5 and vines infested using Action.
The null hypothesis is
H0 : p1 = p2
p1 - p2 = 0
The alternative hypothesis is
Ha : p1 ≠ p2
p1 - p2 ≠ 0
it is a two tailed test
Sample proportion = x/n
Where
x represents number of success(number of complaints)
n represents number of samples
For vines infested using Pernod 5,
x1 = 26
n1 = 410
p1 = 26/410 = 0.063
For vines infested using Action,
x2 = 39
n2 = 400
P2 = 39/400 = 0.098
The pooled proportion, pc is
pc = (x1 + x2)/(n1 + n2)
pc = (26 + 39)/(410 + 400) = 0.08
1 - pc = 1 - 0.08 = 0.92
z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)
z = (0.063 - 0.098)/√(0.08)(0.92)(1/410 + 1/400) = - 0.035/0.019066
z = - 1.84
Since it is a two tailed test, the curve is symmetrical. We will look at the area in both tails. Since it is showing in one tail only, we would double the area
From the normal distribution table, the area below the test z score in the left tail 0.033
We would double this area to include the area in the right tail of z = 1.84 Thus
p = 0.033 × 2 = 0.066
By using the p value,
Since alpha, 0.01 < than the p value, 0.066, then we would fail to reject the null hypothesis.
Therefore, At a 1% level of significance, we cannot conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action
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