It is reported that 70% of car buyers who recently purchased Japanese-made cars were "extremely satisfied" with their purchase, 15% were "somewhat satisfied," 10% were "somewhat unsatisfied," and the rest were "extremely unsatisfied." In a random sample of 100 recent buyers of American-made cars, 55 said they were "extremely satisfied" with their purchase, 20 said they were "somewhat satisfied," 15 said they were "somewhat unsatisfied," and 10 said they were "extremely unsatisfied." You conduct a chi-square goodness-of-fit test using these sample results to test a null hypothesis that the population of recent American car buyers has the same satisfaction levels regarding their purchase as recent Japanese car buyers.The significance level for the test is 5%. Report the critical chi-square value for the test.
A)11.345
B)6.251
C)12.838
D)7.815

Question

Quizplus · Accepted Answer

The chi-square goodness-of-fit test compares the observed frequencies from the sample to the expected frequencies derived from the null hypothesis. Since there are four categories of satisfaction levels, there are 4 - 1 = 3 degrees of freedom. At a 5% significance level, the critical value for 3 degrees of freedom is 7.815.

It Is Reported That 70% of Car Buyers Who Recently