An article reported on a study in which each of 13 workers was provided with bot

Question

An article reported on a study 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 energy expenditure [kcal/kg(subject)/lb(clay)].

Do these data provide convincing evidence that the mean energy expenditure using the conventional shovel exceeds that using the perforated shovel? Test the relevant hypotheses using a significance level of 0.05. (Use a statistical computer package to calculate the P-value. Use conventional perforated. Round your test statistic to two decimal places and your P-value to three decimal places.)

Worker: 1 2 3 4 5 6 7 Conventional: 0.0016 0.0012 0.0018 0.0022 0.001 0.0016 0.0028 Perforated: 0.0016 0.001 0.0019 0.0013 0.0011 0.0017 0.0024 Worker: 8 9 10 11 12 13 Conventional: 0.0023 0.0015 0.0014 0.0023 0.0017 0.002 Perforated: 0.0023 0.0013 0.0013 0.0017 0.0015 0.0013

Explanation / Answer

Below are the null and alternate hypothesis

From the given data we have

Standard Error = 0.00018

DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }

DF = 23

p-value = 0.3653

As p-value is greater than significance level of 0.05, we fail to reject the null hypothesis.

This means there are not sufficienct evidence to conclude that conventional shovel requires more energy

Null Hypothesis Alternate Hypothesis H0: 1 - 2 <= 0 Ha: 1 - 2 > 0

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