Question

USA Today ("Hybrid Car Sales Rose 81% Last Year," April 25, 2005) reported the top five...

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
Ha: H0 is not true.

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

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

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

.H0: p1 = 204.93, p2 = 42.642, p3 = 35.19, p4 = 99.36, p5 = 31.878
Ha: 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.

Homework Answers

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.

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