Compare the standard error from the StatCrunch output in the second table to the standard error obtained in the first table. How did the different study designs affect the outcome of each hypothesis test? Answer these in two or three sentences.

Table 1

Paired T hypothesis test: HD = H1 - H2: Mean of the difference between Carbon and Steel He : HD = 0 HA : HD # 0 Hypothesis test results: Difference Mean Std. Err. DF T-Stat P-value Carbon - Steel -1.6647059 0.41364068 16 -4.0245216 0.001Two sample T hypothesis test: M1: Mean of Carbon H2: Mean of Steel H1 - H2: Difference between two means Ho : H1 - H2 = 0 HA : HI - 12 # 0 (without pooled variances) Sample Statistics: Sample n Mean Std. dev. Carbon 27 18.540741 4.3575098 Steel 31 20.496774 5.0872051 Hypothesis test results: Difference Sample Diff. Std. Err. DF T-Stat P-value H1 - M2 -1.9560335 1.2401947 55.988789 -1.5771987 0.1204