A major car manufacturer was interested in whether its midsize car was selling consistently in two markets with respect to the annual income of the car purchasers. Five-hundred new car buyers in Chicago and Miami were surveyed. In Chicago, the following pattern was observed:
< $20,000 5%;
$20,000-$29,999 0%;
$30,000-$39,999 40%;
$40,000-$49,999 30%;
≥ $50,000 5%.
Among those surveyed in Miami, 20 earned under $20,000; 70 earned between $20,000 and $30,000; 265 earned between $30,000 and $40,000; 125 earned between $40,000 and $50,000; and 20 earned more than $50,000.
(1) What are the expected numbers of car purchasers for each income group if Miami sales among income groups were consistent with Chicago's?
(2) The chi-square test was used to check whether Miami sales among income groups were consistent with Chicago's. The appropriate degrees of freedom for the chi-square test would be
(3) Using the data provided, the calculated value of x2-?
(4) What is the rejection region of the chi-square distribution when the significance level is 0.05?
(5) What is the conclusion of the test when the significance level is 0.05?