Answer:
Step-by-step explanation:
Corresponding true average energy expenditure of shovel with conventional blade and true average energy expenditure of shovel with perforated blades form matched pairs.
The data for the test are the differences between the true average energy expenditures of the shovels.
μd = true average energy expenditure of shovel with conventional blade minus true average energy expenditure of shovel with perforated blades.
Conventional perforated diff
0.0011 0.0011 0
0.0014 0.0010 0.0004
0.0018 0.0019 -0.0001
0.0022 0.0013 0.0009
0.0010 0.0011 -0.0001
0.0016 0.0017 -0.0001
0.0028 0.0024 0.0004
0.0020 0.002 0
0.0015 0.0013 0.0002
0.0023 0.0017 0.0006
0.0017 0.002 -0.0003
0.0020 0.0013 0.0007
0.0014 0.0013 0.0001
Sample mean, xd
= (0 + 0.0004 - 0.0001 + 0.0009 - 0.0001 - 0.0001 + 0.0004 + 0 + 0.0002 + 0.0006 - 0.0003 + 0.0007 + 0.0001)/13 = 0.0002077
xd = 0.0002077
Standard deviation = √(summation(x - mean)²/n
n = 13
Summation(x - mean)² = (0 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2+ (0.0009 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2 + ( - 0.0001 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (0 - 0.0002077)^2 + (0.0002 - 0.0002077)^2 + (0.0006 - 0.0002077)^2 + (- 0.0003 - 0.0002077)^2 + (0.0007 - 0.0002077)^2 + (0.0001 - 0.0002077)^2 = 0.00000158923
Standard deviation = √(0.00000158923/13
sd = 0.00035
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 13 - 1 = 12
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (0.0002077 - 0)/(0.00035/√13)
t = 2.14
We would determine the probability value by using the t test calculator.
p = 0.027
Since alpha, 0.05 > than the p value, 0.027, then we would reject the null hypothesis. Therefore, at 5% significance level, we can conclude that the true average energy expenditure using the conventional shovel does not exceed that using the perforated shovel.
