1. Seventy 5th-grade students were randomly selected for a study. Reading and arithmetic abilities (on 100-point assessments) were recorded for each student. Denote these variables X1 and X2, respectively. The sample mean and covariance matrix for the data are 79.0 = and S = 25.0 2.3 71.1 2.3 15.1 (a) 2pts What is the population of interest in this study? What is the sample? (b) 3pts Consider the following two confidence intervals 79.0 + t.05 (69) 25.0 70 and 71.1 + t.05 (69) / 15.1 70 where t.05 (69) is the upper .05 percentile of the t-distribution with 69 degrees of freedom. What is the individual confidence level for each? Without modification, what confidence level could be applied to them simultaneously? (c) 3pts Are these two variables significantly correlated? Conduct an appropriate hypoth- esis test with critical value 2.0