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". 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".