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 | 250 |
Virginia | 54 |
Washington | 31 |
Florida | 31 |
Maryland | 31 |
Total | 397 |
(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 = 0.495
Ha: H0 is not
true.H0: p1 =
p2 = p3 =
p4 = p5 = 0.2
Ha: H0 is not
true. H0:
p1 = p2 =
p3 = p4 =
p5 = 397
Ha: H0 is not
true.H0: p1 = 196.515,
p2 = 40.891, p3 = 33.745,
p4 = 95.28, p5 =
30.569
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.
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?
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.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.Do not reject H0. There is convincing evidence to conclude that hybrid sales are not proportional to population size for the five states listed.
The statistical software output for this problem is :
H0: p1 = 0.495, p2 = 0.103,
p3 = 0.085, p4 = 0.240, p5 =
0.077
Ha: H0 is not true.
Test statistics = 62.35
P-value = 0.0000
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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