An engineer examined the ultimate load (in kN) for two different types of beams as given in the table below. Assume the underlying distributions are normally distributed. Observation Number 1 2 3 4 5 6 Fiberglass Beam 33 35 34 32 31 29 Carbon Composite Beam |43 46 45 41 42 36 a) What are the null and alternate hypotheses for assessing if the Carbon Composite Beam has a greater ultimate load than the Fiberglass beam? b) Assess whether the null hypothesis should be accepted or rejected by determining the test value and comparing to the critical region. Use a level of significance of aa = 0.01. c) Construct the 99% confidence interval for difference in means between the two types of beams. d) Does the upper limit of the interval you calculated in (c) provide the same comparison as the hypothesis test you performed in (b)? Justify your