deer = read.csv("Deer.csv")
iris <- read.csv("iris.csv")
aragorn = rnorm(50, mean=180, sd=10)
gimli = rnorm(50, mean=132, sd=15)
legolas = rnorm(50, 195, 15)Strange_m9_quarto
Module 9 Exercise - 06/15/2025
Set working directory and load data:
1. Run a t-test to compare the Legolas actors to the set of Aragorns and then the set of Gimlis. Do you find evidence for significant differences?
Legolas vs Aragorn:
t.test(legolas, aragorn, alternative = "two.sided")
Welch Two Sample t-test
data: legolas and aragorn
t = 7.2457, df = 88.581, p-value = 1.519e-10
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
13.47492 23.65874
sample estimates:
mean of x mean of y
195.4503 176.8835 When comparing the Legolas and Aragorn datasets, we recieved a p-value of 2.272e-06, which is smaller than the significance level of 0.05. Therefore, we reject the null hypothesis. There is a statistically significant difference between the mean heights of Aragorn actors and Legolas actors.
Legolas vs Gimli:
t.test(legolas, gimli, alternative = "two.sided")
Welch Two Sample t-test
data: legolas and gimli
t = 20.771, df = 97.921, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
56.24039 68.12213
sample estimates:
mean of x mean of y
195.4503 133.2690 When comparing the Legolas and Gimli datasets, we recieved a p-value of < 2.2e-16, which is much smaller than the significance level of 0.05. Therefore, we reject the null hypothesis. There is a statistically significant difference between the mean heights of Legolas actors and Gimli actors.
2. Re-run the variance test (F-test) to compare the group of Gimli and Legolas actors.
var.test(gimli, legolas)
F test to compare two variances
data: gimli and legolas
F = 1.0585, num df = 49, denom df = 49, p-value = 0.8432
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.6006459 1.8651906
sample estimates:
ratio of variances
1.058451 Do these groups have different variance?
No, the Gimli group and the Legolas group do not have statistically significant differences in variance. We fail to reject the null hypothesis. The p-value is 0.3895, which is not less than the significance level of 0.05. Furthermore, the null hypothesis’s variance ratio of 1 falls between the confidence interval of 0.7267759 - 2.2568634.
4. Using the deer dataset and the chisq.test() function:
deer = read.csv("Deer.csv")Test if there are significant differences in the number of deer caught per month.
table(deer$Month)
1 2 3 4 5 6 7 8 9 10 11 12
256 165 27 3 2 35 11 19 58 168 189 188 chisq.test(table(deer$Month))
Chi-squared test for given probabilities
data: table(deer$Month)
X-squared = 997.07, df = 11, p-value < 2.2e-16Yes, there are significant differences in the number of deer caught per month. The p-value of the chi-squared test is < 2.2e-16, which is much less than the significance level of 0.05, confirming the statistical significance of the differences in deer caught per month.
Test if the cases of tuberculosis are uniformly distributed across all farms.
table(deer$Farm, deer$Tb)
0 1
AL 10 3
AU 23 0
BA 67 5
BE 7 0
CB 88 3
CRC 4 0
HB 22 1
LCV 0 1
LN 28 6
MAN 27 24
MB 16 5
MO 186 31
NC 24 4
NV 18 1
PA 11 0
PN 39 0
QM 67 7
RF 23 1
RN 21 0
RO 31 0
SAL 0 1
SAU 3 0
SE 16 10
TI 9 0
TN 16 2
VISO 13 1
VY 15 4chisq.test(table(deer$Farm, deer$Tb))Warning in chisq.test(table(deer$Farm, deer$Tb)): Chi-squared approximation may
be incorrect
Pearson's Chi-squared test
data: table(deer$Farm, deer$Tb)
X-squared = 129.09, df = 26, p-value = 1.243e-15