Provide a step by step breakdown of all working and show the steps for the R codes in R Studio. Task 1. Statistical inference with the mean obtained from a sample In this case, only the tests for the first two ventilators will be performed, because they are the ones that have yielded the worst and best results in the tests, respectively. The aim is to check whether or not the values obtained from the tests support the data provided by the manufacturer (null hypothesis). It should be noted that the mean obtained from the simulator is the result of 12 tests. Given the following data tables: Ventilator 1 Mean Air Pressure Ventilator Mean 74.86 Ventilator Standard Deviation 6.81 Mean Obtained in the Test 67.38 Sample Size 12 Ventilator 2 Mean Air Pressure Ventilator Mean 59.66 Ventilator standard Deviation 1.65 Mean Obtained in the Test 56.62 Sample Size 12 Determine the null and alternative hypotheses according to the data obtained from the simulation (consider that the standard deviation of the simulation is the one obtained from the sample). Using the critical value method and =0.05, calculate the z-score z_α and the acceptance region for the data obtained from the simulation tests. Validate the results obtained above using the functions used by R for doing the corresponding tests. Indicate whether H0 is accepted or refuted. Is the sample size considered suitable, what must it be to minimize the error of the mean to 1.5? Can any conclusions be drawn from the sample sizes and tests performed?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 22PFA

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Provide a step by step breakdown of all working and show the steps for the R codes in R Studio.

Task 1. Statistical inference with the mean obtained from a sample

In this case, only the tests for the first two ventilators will be performed, because they are the ones that have yielded the worst and best results in the tests, respectively.

The aim is to check whether or not the values obtained from the tests support the data provided by the manufacturer (null hypothesis). It should be noted that the mean obtained from the simulator is the result of 12 tests.

Given the following data tables:

Ventilator 1	Mean Air Pressure
Ventilator Mean	74.86
Ventilator Standard Deviation	6.81
Mean Obtained in the Test	67.38
Sample Size	12

Ventilator 2	Mean Air Pressure
Ventilator Mean	59.66
Ventilator standard Deviation	1.65
Mean Obtained in the Test	56.62
Sample Size	12

Determine the null and alternative hypotheses according to the data obtained from the simulation (consider that the standard deviation of the simulation is the one obtained from the sample).

Using the critical value method and =0.05, calculate the z-score z_α and the acceptance region for the data obtained from the simulation tests.

Validate the results obtained above using the functions used by R for doing the corresponding tests.

Indicate whether H0 is accepted or refuted.

Is the sample size considered suitable, what must it be to minimize the error of the mean to 1.5? Can any conclusions be drawn from the sample sizes and tests performed?

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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