Question

task 2
applying a level of significance
in this task, youll study the data from two experiments. for each data set, you will determine whether the difference of means between the treatment group and the control group is statistically significant and interpret the result in the context of the situation.
question 1
researchers want to find a way to increase the growth rate of corn so it can be harvested more often. to test the effectiveness of a new type of spray fertilizer, plants grown from 200 corn seeds were divided equally into two groups: a treatment group and a control group. the treatment group was frequently sprayed with the new type of fertilizer. the growth in centimeters of each corn plant was noted before and after the treatment.
the results showed that the mean change in the growth rate by the treatment group is 8 points more than that of the control group. to test whether the results could be explained by random chance, researchers treated a table that summarizes the results of 1,000 re - randomizations of the data with differences of means rounded to the nearest 2 points.
consider the significance level to be set at 5%, so results less than 5% can be considered statistically significant.
treatment group mean - control group mean frequency
-12 1
-10 10
-8 28
-6 58
-4 125
-2 184
0 201
2 186
4 114
6 57
8 26
10 8
12 2
part a
question
determine the probability of the treatment groups mean being greater than the control groups mean by 8 points or more. then complete the statements.
the significance level is set at 5%, and the probability of the result is %, which is the significance level. the result is

Explanation:

Step1: Identify relevant frequencies

We need to find the frequencies for differences of 8, 10, and 12 (since we want the treatment - group mean to be greater than the control - group mean by 8 points or more). The frequencies are 26, 8, and 2 respectively.

Step2: Calculate total frequency

The total number of re - randomizations is 1000.

Step3: Calculate probability

The probability $P$ is the sum of the relevant frequencies divided by the total number of re - randomizations. $P=\frac{26 + 8+2}{1000}=\frac{36}{1000}=3.6\%$.

Answer:

The significance level is set at 5%, and the probability of the result is 3.6%, which is less than the significance level. The result is statistically significant.