Question

Provide an example of a two sample (independent) t test in scientific research.

Answer 1

Example of a two-sample  (independent) t-test.

1) Over a period of time, several samples of water were collected from each of two ponds in the Bahamas to compare salinity values (in parts per thousand).

Pond A: 37, 37.2, 37.3, 36.7, 37.7, 37, 38.8, 36.7, 37.3, 37.4, 37.3, 37.5

Pond B: 38.6, 40, 39.5, 38.8, 38.7, 38.5, 38.5, 39.2, 38.2, 39

Use a 0.05 significance level to test the claim that the two ponds have the same mean salinity value. (Use pond A - pond B)

Solution:

n1 = 12

= 37.325

s1 = 0.552885

n2 = 10

= 38.9

s2 = 0.539547

Claim: The two ponds have the same mean salinity value.

The null and alternative hypothesis is

For doing this test first we have to check the two groups have population variances are equal or not.

Null and alternative hypothesis is

Test statistic is

F = largest sample variance / Smallest sample variances

F = 0.305682 / 0.291111 = 1.05

Degrees of freedom => n1 - 1 , n2 - 1 => 12 - 1 , 10 - 1 => 11 , 9

Critical value = 3.102 ( Using f table)

Critical value > test statistic so we fail to reject null hypothesis.

Conclusion: The population variances are equal.

So we have to use here pooled variance.

Test statistic is

Degrees of freedom = n1 + n2 - 2 = 12 + 10 - 2 = 22

Critical value = 2.074 ( Using t table)

| t | > critical value we reject null hypothesis.

Conclusion: The two ponds have different mean salinity value.

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