The Environmental Protection Agency releases figures on urba

The Environmental Protection Agency releases figures on urban air soot in selected cities in the United States. For the city of St. Louis, the EPA claims that the average number of micrograms of suspended particles per cubic meter of air is 82. Suppose St. Louis officials have been working with business, commuters, and industries to reduce this figure. These city officials hire an environmental company to take random measures of air soot over a period of several weeks. The resulting data follow. Assume that population standard deviation is 9.184. Use these data to determine whether the urban air soot in St. Louis is significantly lower than it was when the EPA conducted its measurements. Let a = 0.01. If the null hypothesis is rejected, discuss the substantive hypothesis. What are the appropriate hypotheses H What is your test statistic value? (keep 2 decimal digits) What is your p-value? (keep 4 decimal digits) What is your decision?

Solution

a)

Ho: u = 82
Ho: u < 82 [as they are hoping to reduce the mean]

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b)

Getting the mean, X,      
      
X = Sum(x) / n      

Sum(x) =    2500  

As n = 32,
      
Thus,      

X =    78.125   [ANSWER, SAMPLE MEAN]

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c)

As we can see, this is a    left   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    78.125          
uo = hypothesized mean =    82          
n = sample size =    32          
s = standard deviation =    9.184          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.38679336 = -2.39 [ANSWER]          

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d)

Also, the p value is              
              
p =    0.0085   [ANSWER]

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As p < 0.01, we   REJECT THE NULL HYPOTHESIS.

There is a significant reduction in the avergae urban air soot. [conclusion]