A random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen, resulting in the accompanying data (from “Engineering Properties of Soil,” Soil Sci., 1998: 93–102).
Notice that these values are provided in percentage terms (i.e. what is noted as 1.10 is 1.1%)
dirt <- c(1.10, 5.09, 0.97, 1.59, 4.60,
0.32, 0.55, 1.45, 0.14, 4.47,
1.20, 3.50, 5.02, 4.67, 5.22,
2.69, 3.98, 3.17, 3.03, 2.21,
0.69, 4.47, 3.31, 1.17, 0.76,
1.17, 1.57, 2.62, 1.66, 2.05 )
(a) Create a plot of this dirt data that examines the distribution of this sample. Does a t-test seem appropriate in this case? Why or why not?
(b) Compute the values for the sample average, sample standard deviation, and standard error of the mean.
(c) Either by hand (eww...dirty), or using the built-in function t.test conduct a test for whether this sample is drawn from a population with a percentage of organic matter equal to 3%. Because we have only a few samples, suppose that you would be willing to reject the null hypothesis if a p-value is smaller than or equal to 0.10.
library(ggplot2)library(patchwork)dirt_density <- ggplot() + aes(x=dirt) + geom_density()dirt_qq <- ggplot() + aes(sample=dirt) + geom_qq() + geom_qq_line()dirt_density / dirt_qqsample_mean <- mean(dirt) sample_sd <- sd(dirt) sample_sem <- sd(dirt) / sqrt(length(dirt))## By Hand test_statistic <- (sample_mean - 3) / sample_sem 2 * pt(-1*abs(test_statistic), df=length(dirt)-1)## Using built in t.test(dirt, mu=3)