Two designs for a labratory are to be compared with respect to average amount of light produced on table surfaces. Forty independent measurements (in footcandles) are taken in each lab design, for a total of 80 measurements for the whole experiment. The results are as follows: design 1: average x = 28.9, sample variances (s^2) = 15.1, sample size (n) = 40. Design 2: Average x = 32.6, sample variances (s^2) = 15.8, sample size (n) = 40. Is there sufficent evidence to suggest that the designs differ with respect to average amount of light produced? A. (i) state the null and alternative hypothesis. (ii) calculate the appropriate test statistic value. (iii) State the critical values for this test. (iv) state your conclusion to test based on the problem description (a=0.01). B. Calculate and interpret a 99% confidence intervl for the difference between the average amount of light produced in each lab. What conclusions can you make about the hypotheses?