Question

A newspaper 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	253
Virginia	59
Washington	37
Florida	32
Maryland	32
Total	413

(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 website 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

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

χ² =

What is the P-value for the test? (Use technology to calculate the P-value. Round your answer to three decimal places.)

P-value =

What can you conclude?

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

Chi square Goodness of fit

Table:

Test statistic:

Degrees of Freedom: k-1 = 5-1 = 4

Where, K = Number of Categories = 5

P-value: 0.000    ................Using Chi square table

Conclusion:

P-value < , i.e 0.0000 < 0.01, That is Reject Ho at 1% level of significance.

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