USA Today (\"Hybrid Car Sales Rose 81% Last Year,\" April 25, 2005) reported the
ID: 3225500 • Letter: U
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 254
Virginia 61
Washington 31
Florida 35
Maryland 35
Total 416
(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 2 goodness-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.
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 = 205.92, p2 = 42.848, p3 = 35.36, p4 = 99.84, p5 = 32.032
Ha: H0 is not true.H0: p1 = p2 = p3 = p4 = p5 = 0.495
Ha: H0 is not true. H0: p1 = p2 = p3 = p4 = p5 = 416
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 = p2 = p3 = p4 = p5 = 0.2
Ha: H0 is not true.
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 =
What can you conclude?
1)Reject H0. There is not enough evidence to conclude that hybrid sales are not proportional to population size for the five states listed.
2)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.
3) Do not reject H0. There is convincing evidence to conclude that hybrid sales are not proportional to population size for the five states listed.
4)Reject H0. There is convincing evidence to conclude that hybrid sales are not proportional to population size for the five states listed.
Explanation / Answer
Ha: H0 is not true.H0: p1 = 0.495, p2 = 0.103, p3 = 0.085, p4 = 0.240, p5 = 0.077
X2 =61.8382
p vlaue=0.0000
4)Reject H0. There is convincing evidence to conclude that hybrid sales are not proportional to population size for the five states listed.
observed Expected Chi square Probability O E=total*p =(O-E)^2/E California 0.495 254.000 205.92 11.23 Virginia 0.103 61.000 42.85 7.69 Washington 0.085 31.000 35.36 0.54 Florida 0.24 35.000 99.84 42.11 Maryland 0.077 35.000 32.03 0.28 416 416 61.84Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.