Question

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.

State	Observed Frequency
California	255
Virginia	56
Washington	37
Florida	33
Maryland	33
Total	414

(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 χ² goodness-of-fit test and a significance level of

α = 0.01

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

State	2004 Population	Population Proportion
California	35,842,038	0.495
Virginia	7,481,332	0.103
Washington	6,207,046	0.085
Florida	17,385,430	0.240
Maryland	5,561,332	0.077
Total	72,477,178

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.

H₀: p₁ = p₂ = p₃ = p₄ = p₅ = 0.2
H_a: H₀ is not true.

H₀: p₁ = p₂ = p₃ = p₄ = p₅ = 0.495
H_a: H₀ is not true.    

H₀: p₁ = p₂ = p₃ = p₄ = p₅ = 414
H_a: H₀ is not true.

H₀: p₁ = 0.495, p₂ = 0.103, p₃ = 0.085, p₄ = 0.240, p₅ = 0.077
H_a: H₀ is not true

.H₀: p₁ = 204.93, p₂ = 42.642, p₃ = 35.19, p₄ = 99.36, p₅ = 31.878
H_a: H₀ is not true.

Calculate the test statistic. (Round your answer to two decimal places.)
χ² =  

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

What can you conclude?

Reject H₀. There is not enough evidence to conclude that hybrid sales are not proportional to population size for the five states listed.

Do not reject H₀. There is not enough evidence to conclude that hybrid sales are not proportional to population size for the five states listed.   

Do not reject H₀. There is convincing evidence to conclude that hybrid sales are not proportional to population size for the five states listed.

Reject H₀. There is convincing evidence to conclude that hybrid sales are not proportional to population size for the five states listed.

Answer 1

a) Correct answer:
H0: p1 = 0.495, p2 = 0.103, p3 = 0.085, p4 = 0.240, p5 = 0.077
Ha: H0 is not true

b) From the given data

	Observed		Expected
	Freq (Oi)	Probability	Freq. (Ei)	(Oi-Ei)^2 /Ei
California	35842038	0.495	35876203.1	32.5356
Virginia	7481332	0.103	7465149.33	35.0802
Washington	6207046	0.085	6160560.13	350.7694
Florida	17385430	0.240	17394522.7	4.7531
Maryland	5561332	0.077	5580742.71	67.5135
Total:	72477178		72477178	490.6518

Degrees of freedom: 5-1 = 4

Test Statistic, X^2: 490.6518

c) P-Value: 0.0000

since P-value < alpha 0.01 so we reject H0

Correct answer: Option (D) Reject H₀. There is convincing evidence to conclude that hybrid sales are not proportional to population size for the five states listed.