A chi-square test for homogeneity was conducted to investigate whether the four high schools in a school district have different absentee rates for each of four grade levels. The chi-square test statistic and p-value of the test were 19.02 and 0.025, respectively. Which of the following is the correct interpretation of the p-value in the context of the test? A) Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or smaller. B) Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger. C) Assuming that each high school has a different absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger. D) There is a 2.5 percent chance that the absentee rate for each grade level at the four schools is the same. E) There is a 2.5 percent chance that the absentee rate for each grade level at the four schools is different.
A chi-square test for homogeneity was conducted to investigate whether the four high schools in a school district have different absentee rates for each of four grade levels. The chi-square test statistic and p-value of the test were 19.02 and 0.025, respectively. Which of the following is the correct interpretation of the p-value in the context of the test?
A) Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or smaller.
B) Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger.
C) Assuming that each high school has a different absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger.
D) There is a 2.5 percent chance that the absentee rate for each grade level at the four schools is the same.
E) There is a 2.5 percent chance that the absentee rate for each grade level at the four schools is different.
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Answer: B) Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger.
Explanation: The p-value indicates the probability of observing a chi-square statistic as extreme as 19.02 or more, assuming that the null hypothesis (same absentee rates) is true.
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