A certain chemical pollutant in the Genesee River has been c

A certain chemical pollutant in the Genesee River has been constant for several years with mean 34 ppm (parts per million) and standard deviation 8 ppm. A group of factory representatives whose companies discharge liquids into the river is now claiming that they have lowered the average with improved filtration devices. A group of environmentalists will test to see if this is true at the 4% level of significance. Assume that their sample of size 50 gives a mean of 32.5 ppm. Perform a hypothesis at the 4% level of significance and state your decision. a. H0: b. H alpha: c. Test Statistic: Check assumptions. d. Calculate the test statistic: e. p-value: f. Decision: Reject or Do Not Reject the null hypothesis, H0. g. Conclusion in context of the problem:

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   34  

b)

Ha:    u   <   34  

c)

We use Z STATISTIC, as n > 30.

d)
              
As we can see, this is a    left   tailed test.      
              
Getting the test statistic, as              
              
X = sample mean =    32.5          
uo = hypothesized mean =    34          
n = sample size =    50          
s = standard deviation =    8          
              
Thus, z = (X - uo) * sqrt(n) / s =    -1.325825215 [ANSWER]

************************
          
E)
              
Also, the left tailed p value is, by table/technology,              
              
p =    0.092448799   [ANSWER]

****************      
              
f)

As P > 0.04, we DO NOT REJECT the null hypothesis.

*************************

G)

There is no significant evidence that the new mean concentration of the chemical pollutant in the Genesee River is less than 34 ppm. [CONCLUSION]