It is estimated that the average test score for a statistics exam will be µ = 70, with a variance of σ 2 = 12. in a random sample of 8 students, the test scores are 65, 73, 74, 68, 70, 74, 69, 71, giving us the sample statistics ¯x = 70.5 and s 2 = 10. assume a normal distribution of scores. answer the following questions to determine if you would agree with the assumption of σ 2 or not. (a) use the sampling distribution of s 2 to find the value of χ 2 corresponding to what is seen in the data, and our assumption about the population variance. round your answer to 3 decimals. (b) find χ 2 0.975(df), where df is the degrees of freedom value corresponding to the statistic from part 7a. (c) find χ 2 0.025(df), where df is the degrees of freedom value corresponding to the statistic from part 7a. (d) would you agree with our assumption that the population variance is σ 2 = 12? why or why not?