Problem 3There are two primary means to drill holes in rock: dry drilling and wet drilling. With dry drilling,compressed air is used to flush the cuttings out of the drill bit. With wet drilling, a liquid is used.The time required (in minutes) to drill a hole of a particular depth was acquired and found in(the image attached). Assume similar variances for the two drilling methods. Is mean drilling timefor the wet drilling method significantly shorter with 95% confidence? Use the ?-valueapproach. The table provides data comparing measurements from dry drilling and wet drilling methods. There are two columns, each representing a different drilling method.**Columns:**- **Dry Drilling (Column A):** - Row 2: 7.27 - Row 3: 9.65 - Row 4: 9.04 - Row 5: 9.87 - Row 6: 8.47 - Row 7: 9.18 - Row 8: 8.14 - Row 9: 7.5 - Row 10: 8.04 - Row 11: 9.89 - Row 12: 9.02 - Row 13: 9.39- **Wet Drilling (Column B):** - Row 2: 6.07 - Row 3: 5.49 - Row 4: 7.62 - Row 5: 6.65 - Row 6: 5.88 - Row 7: 7.98 - Row 8: 7.04 - Row 9: 7.72 - Row 10: 7.8 - Row 11: 5.99This dataset can help in analyzing the differences in performance or outcomes between dry and wet drilling methods.

Given that: Confidence level = 95% Dry dilling Wet drilling 7.27 6.07 9.65 5.49 9.04 7.62…

Answered: Problem 3 There are two primary means…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Problem 3
There are two primary means to drill holes in rock: dry drilling and wet drilling. With dry drilling,
compressed air is used to flush the cuttings out of the drill bit. With wet drilling, a liquid is used.
The time required (in minutes) to drill a hole of a particular depth was acquired and found in
(the image attached). Assume similar variances for the two drilling methods. Is mean drilling time
for the wet drilling method significantly shorter with 95% confidence? Use the ?-value
approach.

The table provides data comparing measurements from dry drilling and wet drilling methods. There are two columns, each representing a different drilling method.

**Columns:**
- **Dry Drilling (Column A):**
- Row 2: 7.27
- Row 3: 9.65
- Row 4: 9.04
- Row 5: 9.87
- Row 6: 8.47
- Row 7: 9.18
- Row 8: 8.14
- Row 9: 7.5
- Row 10: 8.04
- Row 11: 9.89
- Row 12: 9.02
- Row 13: 9.39

- **Wet Drilling (Column B):**
- Row 2: 6.07
- Row 3: 5.49
- Row 4: 7.62
- Row 5: 6.65
- Row 6: 5.88
- Row 7: 7.98
- Row 8: 7.04
- Row 9: 7.72
- Row 10: 7.8
- Row 11: 5.99

This dataset can help in analyzing the differences in performance or outcomes between dry and wet drilling methods.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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