USA Today Hybrid Car Sales Rose 81 Last Year April 25 2005 r

USA Today (\"Hybrid Car Sales Rose 81% Last Year,\" April 25, 2005) reported the top five states for sales of hybrid cars in 2004 as California, Virginia, Washington, Florida, and Maryland. Suppose that each car in a sample of 2004 hybrid car sales is classified by state where the sale took place. Sales from states other than the top five were excluded from the sample, resulting in the accompanying table.

(The given observed counts are artificial, but they are consistent with hybrid sales figures given in the article.)

The 2004 population estimates from the Census Bureau web site are given in the accompanying table. The population proportion for each state was computed by dividing each state population by the total population for all five states. Use the ²goodness-of-fit test and a significance level of

= 0.01

to test the hypothesis that hybrid sales for these five states are proportional to the 2004 population for these states.

Let p₁, p₂, p₃, p₄, and p₅ be the actual population proportions of 2004 for the five states in the following order: California, Virginia, Washington, Florida, Maryland.

State the null and alternative hypotheses.

Calculate the test statistic. (Round your answer to two decimal places.)
² =  

What is the P-value for the test? (Round your answer to four decimal places.)
P-value =  

Solution

A)

OPTION B:

H0: p1 = 0.495, p2 = 0.103, p3 = 0.085, p4 = 0.240, p5 = 0.077
Ha: H0 is not true. [ANSWER]

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b)

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
254   203.94   12.28794547  
53   42.436   2.629797719  
37   35.02   0.111947459  
34   98.88   42.57093851  
34   31.724   0.163288866  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    57.76391803   [ANSWER, TEST STATISTIC]

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c)
  
          
As df = a - 1,           
          
a =    5      
df = a - 1 =    4      
          
Thus, the p value is          
          
p =    8.5533*10^-12 = 0.0000   [ANSWER]