What is the test statistic

Question

Samples were collected from two ponds in the Bahamas to compare salinity values (in parts per thousand). Several samples were drawn at each site.

Pond 1: 37.01, 37.02, 37.03, 37.71, 37.32, 37.36, 36.75

Pond 2: 38.66, 39.21, 39.05, 38.89, 39.04

Use a 0.050.05 significance level to test the claim that the two ponds have the same mean salinity value.

(a) The test statistic is

Answer 1

First, we need to calculate the sample means and standard deviations for each pond:

Pond 1:

n1 = 7, x̄1 = 37.21, s1 = 0.327

Pond 2:

n2 = 5, x̄2 = 39.01, s2 = 0.368

The formula for the two-sample t-test statistic is:

t = (x̄1 - x̄2) / (sqrt(s1^2/n1 + s2^2/n2))

Plugging in the values, we get:

t = (37.21 - 39.01) / (sqrt(0.327^2/7 + 0.368^2/5))

= -3.24

Therefore, the test statistic is t = -3.24.