Question

2. n = 14 samples are taken from a stream; the mean pollutant level is 16.4 mg/l, and the standard deviation is 5.3. Test the hypothesis that the true mean is no different than the "normal" level of 12.5 mg/l. State the null and alternative hypotheses, and use a Type I error level of 5%.

Answer 1

Q.2) Given that, sample size (n) = 14, sample mean = 16.4 mg/l and sample standard deviation (s) = 5.3

We want to test the hypothesis that the true mean is no different than the "normal" level of 12.5 mg/l.

Therefore, the null and alternative hypotheses are,

H0 : μ = 12.5 mg/l

Ha : μ ≠ 12.5 mg/l

This hypothesis test is a two-tailed test.

Test statistic is,

=> Test statistic = t = 2.753

Degrees of freedom = 14 - 1 = 13

Using t-table we get, t-critical value at significance level of 0.05 with 13 degrees of freedom are, tcrit = ± 2.160

Since, test statistic = 2.753 > 2.160, we reject the null hypothesis (H0).

Conclusion : There is sufficient evidence to conclude that the true mean is different than the "normal" level of 12.5 mg/l.