To find the x2 values that divide the area under the chi-square curve for df=7, one would typically use a chi-square distribution table or a calculator, such as the TI-83/84+, to identify the critical values at the 0.025 and 0.975 quantiles, which corresponds to a middle area of 0.95.
The student is asking about the chi-square (χ2) distribution and how to find the critical values that divide the area under the curve into a middle area representing 95% of the total area, with the two outside areas each representing 2.5% of the total area. The student mentions a degree of freedom (df) of 7 for the chi-square distribution in question.
To solve this, we need to use the chi-square distribution table or a calculator capable of computing chi-square distribution values, such as the TI-83, 83+, or 84+ calculator. The values that we need to find are often referred to as critical values and they represent the points on the curve where the cumulative area to the left of the lower value and to the right of the upper value is 0.025. This leaves the middle 95% of the area under the curve between these two points.
As the question is seeking the chi-square critical values, we can assume the student is familiar with the general properties of the chi-square distribution relevant for their level of statistics coursework. However, they require the specifics of finding the cutoff points. The process would involve first consulting the statistical table for the chi-square distribution with 7 degrees of freedom, or using a calculator with statistical functions, to find the values approximately, which can be denoted as χ2₀₀₂₅ and χ2₀₉⁷⁵ corresponding to the lower and upper critical values, respectively.