A research entomologist is interested in evaluating a new chemical formulation for possible use as a pesticide for controlling fire ants. She decides to compare its performance relative to the most widely used pesticide on the market, AntKiller. Each of the pesticides is applied to 100 containers of fire ants. The new pesticide successfully killed all the fire ants within two hours of application in 65 of the 100 containers. Of the 100 containers treated with AntKiller only 59 had all fire ants killed. (a) Is there significant evidence that the proportion of containers successfully treated by the new formulation is greater than the proportion of containers successfully treated by the formula known as AntKiller? Run the appropriate hypothesis test and give me the hypotheses, code, output, and a nice conclusion for your hypothesis test. (b) Construct a 95% confidence interval on the di erence in the two proportions. Make sure you write your interpretation in the same manner we would do a two sample Independent t-test. Please do not run a two-sample t-test.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A research entomologist is interested in evaluating a new chemical formulation for possible
use as a pesticide for controlling fire ants. She decides to compare its performance relative to
the most widely used pesticide on the market, AntKiller. Each of the pesticides is applied to
100 containers of fire ants. The new pesticide successfully killed all the fire ants within two
hours of application in 65 of the 100 containers. Of the 100 containers treated with AntKiller
only 59 had all fire ants killed.
(a) Is there significant evidence that the proportion of containers successfully treated by the
new formulation is greater than the proportion of containers successfully treated by the formula
known as AntKiller? Run the appropriate hypothesis test and give me the hypotheses,
code, output, and a nice conclusion for your hypothesis test.
(b) Construct a 95% confidence interval on the di erence in the two proportions. Make sure
you write your interpretation in the same manner we would do a two sample Independent
t-test. Please do not run a two-sample t-test.
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