Question

According to data released by the World Bank, the mean PM10 (particulate matter) concentration for the city of Kabul, Afghanistan, in 1999 was 46. Suppose that because of efforts to improve air quality in Kabul, increases in modernization, and efforts to establish environmental-friendly businesses, city leaders believe rates of particulate matter in Kabul have decreased. To test this notion, they randomly sample 12 readings over a one-year period with the resulting readings shown below. Do these data present enough evidence to determine that PM10 readings are significantly less now in Kabul? Assume that particulate readings are normally distributed and that α = .01.

31	44	35	53	57	47
32	40	31	38	53	45

Appendix A Statistical Tables

(Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.)

The value of the test statistic is t = and we either a) reject the null hypothesisfail b) fail to reject the null hypothesis .

Answer 1

Ho :   µ =   46                  
Ha :   µ <   46       (Left tail test)          
                          
Level of Significance ,    α =    0.01                  
sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   9.1237                  
Sample Size ,   n =    12                  
Sample Mean,    x̅ = ΣX/n =    42.1667                  
                          
degree of freedom=   DF=n-1=   11                  
                          
Standard Error , SE = s/√n =   9.1237   / √    12   =   2.6338      
t-test statistic= (x̅ - µ )/SE = (   42.167   -   46   ) /    2.6338   =   -1.46
                                
p-Value   =   0.09   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value>α, Do not reject null hypothesis

test stat = -1.46

b) fail to reject the null hypothesis                       

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