Question

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

H0: the true mean is no different than the "normal" level of 12.5 mg i.e. H0: Mu = 12.5

H1: the true mean is different than the "normal" level of 12.5 mg i.e. H1: Mu not = 12.5

Let the los be alpha = 5%

Test Statistic t = (Sample Mean - Population Mean) / (SD / Sqrt(n))

             = (16.4 - 12.5) / (5.3/sqrt(14))

                       = 2.7533

Critical t:        ±2.1604
P-Value:           0.0164

since t value is not in t critical values and P-value < alpha 0.05, so we reject H0

Thus we conclude that the true mean is different than the "normal" level of 12.5 mg i.e. H0: Mu not = 12.5