Our topic is how a treatment will affect the growth of a plant. The question we are investigating is if the treatment will produce a change in growth in a plant than not using a treatment. Historically, when humans have given growth treatments to plants, they have grown taller. We are running tests to figure out if the treatment produces a change in growth in the plants.
The data we are using is called PlantGrowth. The variables we are using are Weight and Group. We are comparing the control group to the treatment group.
Our Null Hypothesis is: The mean of the control group is equal to the mean of the treatment group.
Our Alternative Hypothesis: The mean of the treatment group is not equal to the mean of the control group.
We will use a significance level of α= 0.05
We are conducting a two-sample t-test to test our hypothesis.
P-Val: .2490
The found P-value is greater than our predetermined significance level of 0.05.
We do not choose to reject the null hypothesis. There is no significant difference in the means.
Since the results from the test confirmed that there was no statistical evidence that the treatment changed the growth of the plants. Moving forward with our research in plant growth, if our goal is to accelerate the growth then we will no longer use this treatment method. We may need to consider searching for a new treatment in the future. The test results of this experiment are essential for moving forward in research. There may have been certain chemicals in the formula that stunted the growth of the plants.
library (MASS)
data("PlantGrowth")
attach(PlantGrowth)
PlantGrowth ## weight group
## 1 4.17 ctrl
## 2 5.58 ctrl
## 3 5.18 ctrl
## 4 6.11 ctrl
## 5 4.50 ctrl
## 6 4.61 ctrl
## 7 5.17 ctrl
## 8 4.53 ctrl
## 9 5.33 ctrl
## 10 5.14 ctrl
## 11 4.81 trt1
## 12 4.17 trt1
## 13 4.41 trt1
## 14 3.59 trt1
## 15 5.87 trt1
## 16 3.83 trt1
## 17 6.03 trt1
## 18 4.89 trt1
## 19 4.32 trt1
## 20 4.69 trt1
## 21 6.31 trt2
## 22 5.12 trt2
## 23 5.54 trt2
## 24 5.50 trt2
## 25 5.37 trt2
## 26 5.29 trt2
## 27 4.92 trt2
## 28 6.15 trt2
## 29 5.80 trt2
## 30 5.26 trt2control <- subset(weight, group == "ctrl")
treatment <- subset(weight, group == "trt1")
mean_c <- mean(control)
mean_t <- mean(treatment)
mean <- mean_t - mean_c
var_c <- var(control)
var_t <- var(treatment)
n <- length(control)
m <- length(treatment)
pooled <- sqrt(((n-1)*var_c + (m-1)*var_t) / (n+m-2))
test_stat <- mean / (pooled * sqrt((1/n)+(1/m)))
p_value <- 2 * pt(test_stat, n+m-2)
p_value ## [1] 0.2490232