Answer:
Comparing the p value with the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the two proportions differes at 10% of significance.
Step-by-step explanation:
Data given and notation
represent the number of infested vines for Pernod5
represent the number of infested vines for Action
sample of Pernod5
sample of Action
represent the proportion of residents of infested vines for Pernod5
represent the proportion of infested vines for Action
z would represent the statistic (variable of interest)
represent the value for the test (variable of interest)
significance level given
Concepts and formulas to use
We need to conduct a hypothesis in order to check if is there is a difference between thw two population proportions, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We need to apply a z test to compare proportions, and the statistic is given by:
(1)
Where
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Calculate the statistic
Replacing in formula (1) the values obtained we got this:
Statistical decision
Since is a two sided test the p value would be:
Comparing the p value with the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the two proportions differes at 10% of significance.