Question

suppose n = 13 samples are taken from a stream; the mean pollutant level is 16.7 mg/l, and the standard deviation is 5.1. Use the p-value approach and a significance level of 0.05 to test the hypothesis that the true mean is no different than the ‘normal’ level of 14.2 mg/l. Write down the null and alternative hypotheses, find the test statistic and the p-value, and state your conclusion.

Answer 1

H0: = 14.2

Ha: 14.2

Test statistics

t = - / S / sqrt(n)

= 16.7 - 14.2 / 5.1 / sqrt(13)

= 1.77

This is test statistics value.

From T table,

Using test statistics t = 1.77 and df = 12 ,

p-value = 0.1021

Since p-value > 0.05 , we do not have sufficient evidence to reject the null hypothesis

We conclude at 0.05 level that we fail to support the claim.