Question

Water quality experts for the forestry service are concerned with the recent environmental problems upstream and would like to test whether the average phosphorous content has risen above 15 parts per billion (ppb). A random sample at 12 different points in the water supply was collected showing a sample average of 16.33 ppb and a sample standard deviation of 2.62 ppb. Conduct a statistical test at the significance level of 5%. You can use either the critical value approach or the p-value approach.

(a) State the null and alternative hypotheses.

(b) Choose between a one-sided and two-sided test.

(c) Decide on the type of test and explain why.

(d) Calculate sample t statistics.

(e) Calculate either the critical value or the p value.

(f) Make a conclusion of the test.

(g) What parametric assumption do you have to make for this test?

Answer 1

Solution :

= 15

=16.33

S =2.62

n = 12

This is the right tailed test .

The null and alternative hypothesis is ,

H0 :    = 15

Ha : > 15

Test statistic = t

= ( - ) / S / n

= (15-16.33) / 2.62 / 12

= 1.758

Test statistic = t = 1.758

The critical value =1.796

P-value =0.0532

= 0.05  

P-value >

0.0532 > 0.05

Fail to reject the null hypothesis .

There is not sufficient evidence to claim that the population mean μ is greater than 15, at the 0.05 significance level.