Carry out a test of hypotheses at signi?cance level .05 to see if true average e

Question

Carry out a test of hypotheses at signi?cance level .05 to see if true average energy expenditure using the conventional shovel exceeds that using the per-forated shovel.

41. Shoveling is not exactly a high-tech activity but will continue to be a required task even in our informa- tion age. The article "A Shovel with a Perforated Blade Reduces Energy Expenditure Required for Digging Wet Clay" (Human Factors, 2010: 492-502) reported on an experiment in which each of 13 workers was provided with both a conventional shovel and a shovel whose blade was perforated with small holes. The authors of the cited article provided the following data on stable energy expenditure [kcal/kg(subject)lb(clay) Worker: Conventional:.0011.0014 .0018.0022 .0010.0016.0028 Perforated: .0011 0010.0019 .0013 .0011 .0017.0024 Worker: Conventional:.0020.0015 0014.0023 .0017.0020 Perforated: 0020 .0013.0013 .0017 .0015 .0013 8 9 10 12 13

Explanation / Answer

H0: There is no difference between means of two groups

H1: conventional mean is greater than per-forated shovel

alpha:5%

Test statistics:

Fromm Excel

t cal=1.3638

COnclsuion:

P value=0.093 >0.05 we accept the H0. Hence the claim is not significant

t-Test: Two-Sample Assuming Unequal Variances Conventional perforated Mean 0.001753846 0.001508 Variance 2.54359E-07 1.69E-07 Observations 13 13 Hypothesized Mean Difference 0 df 23 t Stat 1.363864787 P(T<=t) one-tail 0.092905029 t Critical one-tail 1.713871528 P(T<=t) two-tail 0.185810057 t Critical two-tail 2.06865761

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