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 p-value for the test.
A).0685
B).2234
C).0062
D).0036

Question

Quizplus · Accepted Answer

The chi-square goodness-of-fit test compares the observed frequencies from the sample (American car buyers) to the expected frequencies based on the proportions given for Japanese car buyers. The calculation of the chi-square statistic involves summing the squared differences between observed and expected frequencies, divided by the expected frequencies. Given the significance level of 5%, the p-value of .0062 indicates that there is a statistically significant difference between the satisfaction levels of American and Japanese car buyers, leading to the rejection of the null hypothesis.

It Is Reported That 70% of Car Buyers Who Recently