A newspaper article indicated that 43 percent of cars with black seats are white, 46 percent of cars with black seats are blue, 7 percent of cars with black seats are red, and 4 percent of cars with black seats are black. A test was conducted to investigate whether the color of cars with black seats was consistent with the newspaper article. A random sample of cars of these colors was selected, and the value of the chi-square test statistic was χ2=8.2. Which of the following represents the p-value for the test? A) P(χ2≥8.2)=0.08 B) P(χ2≥8.2)=0.04 C) P(χ2≤8.2)=0.96 D) P(χ2=8.2)=0.00 E) The p-value cannot be calculated because the sample size is not given.
A newspaper article indicated that 43 percent of cars with black seats are white, 46 percent of cars with black seats are blue, 7 percent of cars with black seats are red, and 4 percent of cars with black seats are black. A test was conducted to investigate whether the color of cars with black seats was consistent with the newspaper article. A random sample of cars of these colors was selected, and the value of the chi-square test statistic was χ2=8.2. Which of the following represents the p-value for the test?
A) P(χ2≥8.2)=0.08
B) P(χ2≥8.2)=0.04
C) P(χ2≤8.2)=0.96
D) P(χ2=8.2)=0.00
E) The p-value cannot be calculated because the sample size is not given.
Answer
Answer: B) P(χ2≥8.2)=0.04
Explanation: The p-value represents the probability of observing a chi-square statistic as extreme as or more extreme than the observed value. For χ2 = 8.2, the p-value of 0.04 indicates this probability.
Sourav
