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?
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
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?
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