PART 3 A car mat manufacture been having quality issues with its production. A series of tests were carried out to measure the resulting pH of the most common carpet produced, Type 1, as a good indicator of quality.For the following questions show all calculations and formula used. What is the mean, mode and range of the pH after dyeing?Table – Type 1pH after addition of dye5.105 to 5.35.305 to 5.55.5.05 to 5.75.705 to 5.95.905 to 6.16.105 to 6.36.305 to 6.5No. of samples1578741 For pH after addition of dye calculate the standard deviation, showing your calculations in full. Plot the standard deviation graph in Excel showing the distribution. From your calculations and the data Give the minimum and maximum limits the pH may be, given that the distribution is normal.Calculate the probability that a randomly selected carpet sample will have a PH of (i) 6.1 and (ii) 5.4. Further tests were carried on a large sample of all carpet types and the following distribution was obtained. It is believed that the carpet type does not affect the pH. Test this hypothesis and whether there is a correlation or not. ( Data for 1 type of carpet)pH after addition of dye4.85.15.45.65.76.26.36.66.7No. of samples225753201 Finally present the statistical data you have been investigating a manner that can be understood by non-technical management at the carpet factory.

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Answered: PART 3 A car mat manufacture been…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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PART 3

A car mat manufacture been having quality issues with its production. A series of tests were carried out to measure the resulting pH of the most common carpet produced, Type 1, as a good indicator of quality.

For the following questions show all calculations and formula used.

What is the mean, mode and range of the pH after dyeing?

Table – Type 1

pH after addition of dye	5.105 to 5.3	5.305 to 5.5	5.5.05 to 5.7	5.705 to 5.9	5.905 to 6.1	6.105 to 6.3	6.305 to 6.5
No. of samples	1	5	7	8	7	4	1

For pH after addition of dye calculate the standard deviation, showing your calculations in full.

Plot the standard deviation graph in Excel showing the distribution.

From your calculations and the data

Give the minimum and maximum limits the pH may be, given that the distribution is normal.
Calculate the probability that a randomly selected carpet sample will have a PH of (i) 6.1 and (ii) 5.4.

Further tests were carried on a large sample of all carpet types and the following distribution was obtained. It is believed that the carpet type does not affect the pH. Test this hypothesis and whether there is a correlation or not. ( Data for 1 type of carpet)

pH after addition of dye	4.8	5.1	5.4	5.6	5.7	6.2	6.3	6.6	6.7
No. of samples	2	2	5	7	5	3	2	0	1

Finally present the statistical data you have been investigating a manner that can be understood by non-technical management at the carpet factory.

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

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