Now we turn our attention to the other variable: "length of history\". Unlike "scores\

a. b. c. Now we turn our attention to the other variable: "length of history". Unlike "scores", this new variable "length of history" was seen to follow a normal-like distribution in the Boston pool of applicants. A sub-sample of size 20 revealed an average of 12 and a stanndard deviation of 3 years. To attract younger applicants, the company is debating introducing additional perks for them if the true average "history" is at least 11 years. Conduct a test (Le, write out the null and alternate hypotheses, find the value of the test statistic, the p-value, and reach a decision) at a = 0.05 to check whether this move is necessary. With u representing the true average "length of history", choose one of HO_; = 12 or Ha : u *12. We just need a decision here. Please justify your reasoning. Recall that in the original Boston group of 36 applicants, a regression treating "length of history" as the cause and "scores" as the effect gave a slope estimate of A 1 = 11.23 and the standard deviation of the variable "scores" was 21 units. 53.9% of the proportion of total variability in "scores" was explained by this model. Please find out the variance of the variable "length of history".