Question

A bottled water company acquires its water from two independent sources, X and Y. The company suspects that the sodium content in the water from source X is less than the sodium content for water from source Y. An independent agency measures the sodium content in 20 samples from source X and 10 samples from source Y and stores them in data frame WATER.

Is there statistical evidence to suggest the average sodium content in the water from source X is less than the average sodium content in the water from source Y? Also discuss why t-test is appropriate vs z-test.

The measurements for the sodium values are `mg/L`. Use an α level of 0.05 to test the appropriate hypotheses.

For your convenience the output of t-test is shown below:

Welch Two Sample t-test

data:  sodium by source
t = -1.8589, df = 22.069, p-value = 0.03822
alternative hypothesis: true difference in means is less than 0
95 percent confidence interval:
       -Inf -0.3665724
sample estimates:
mean in group x mean in group y 
           76.4            81.2 

Answer 1

The p-value of the test is:

p-value = 0.0382

Since p-value is less than 0.05 so we reject the null hypothesis. There is statistical evidence to suggest the average sodium content in the water from source X is less than the average sodium content in the water from source Y.

t test is appropriate because population standard deviations are not given.