1. A manufacturer believes that their shovel with a perforated blade requires le

Question

1. A manufacturer believes that their shovel with a perforated blade requires less energy than a traditional shovel when digging in red Virginia clay soil. To test this theory, 13 landscapers were asked to dig a 2 foot hole with each of the shovels and their energy expenditure was measured. The average difference in energy expenditure was 0.0246 with a standard deviation of 0.0331. The difference in energy expenditure is assumed to be normally distributed. What is the 99% interval estimate for the average difference in energy expenditure between the two shovels? a. (-0.003, 0.053) b. (0, 0.049) c. (0.001, 0.048) d. (0.003, 0.046)

Explanation / Answer

The average difference in energy expenditure dbar= 0.0246

standard deviation of difference in energy expenditure sd = 0.0331

standard error of difference sed = sd/ sqrt(n) = 0.0331/ sqrt(13) = 0.00918

here sample size n = 13

tcritical = tdf,alpha = t12, 0.01  = 3.05454

Here,

99% confidence interval = dbar +- tcritical  se0

= 0.0246 +- 3.05454 * 0.00918

= (-0.00506, 0.05264)

= (-0.005, 0.053)

Option (a) is correct.  

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