8.3.130 one sample t-test
The following data represent the concentration of organic carbon (mg/L) collected from organic soil. Construct a 99% confidence interval for the mean concentration of dissolved organic carbon collected from organic soil. (Note: \(\bar x\) = 16.56 mg/L and s = 8.3 mg/L)
Construct a 99% confidence interval for the mean concentration of dissolved organic carbon collected from organic soil.
Since the question gives t-distribution table we will use t-test.
First, we need to get the data from Excel. (The approach below gets the data mannually)
data <- c(14.00, 8.81, 30.91, 19.80, 29.80, 7.40, 14.86, 14.86, 27.10, 20.46, 14.00, 8.09, 16.51, 14.90, 15.35, 5.30, 7.40, 33.67, 9.72, 18.30)To get 99% confidence interval, we run
t.test(data, conf.level = .99)##
## One Sample t-test
##
## data: data
## t = 8.9198, df = 19, p-value = 3.21e-08
## alternative hypothesis: true mean is not equal to 0
## 99 percent confidence interval:
## 11.24988 21.87412
## sample estimates:
## mean of x
## 16.562To get the data in 2 decimal places, we run
print(t.test(data, conf.level = .99), 4)##
## One Sample t-test
##
## data: data
## t = 8.9, df = 19, p-value = 3e-08
## alternative hypothesis: true mean is not equal to 0
## 99 percent confidence interval:
## 11.25 21.87
## sample estimates:
## mean of x
## 16.56
Hope that helps!