What is Ha?Choice Answers:1. The mean of group 1 is not the same as the mean of group 2 2. The mean of group 1 is the same as the mean of group 2 3. The number of errors for 8 hours sleep deprivation is different than the number of errors for 24 hours sleep deprivation 4. The number of errors for 8 hours sleep deprivation is equal to the number of errors for 24 hours sleep deprivation 5. The number of errors for 8 hours sleep deprivation is not different than the number of errors for 24 hours sleep deprivation 6. The number of errors for 8 hours sleep deprivation is not equal to the number of errors for 24 hours sleep deprivation 7. The number of errors for 8 hours sleep deprivation is not the same as the number of errors for 24 hours sleep deprivation 8. The number of errors for 8 hours sleep deprivation is the same as the number of errors for 24 hours sleep deprivation ### Paired Samples Analysis#### Paired Samples StatisticsThis section presents the statistics for errors made after different durations of sleep deprivation:- **Errors after 8 hours sleep deprivation**: - Mean = 6.75 - Sample Size (N) = 20 - Standard Deviation = 2.124 - Standard Error Mean = 0.475- **Errors after 24 hours sleep deprivation**: - Mean = 13.90 - Sample Size (N) = 20 - Standard Deviation = 2.024 - Standard Error Mean = 0.452#### Paired Samples CorrelationsThis analysis shows the correlation between errors after 8 hours and 24 hours of sleep deprivation:- **Correlation (r) = -0.263**- Sample Size (N) = 20- Significance (One-Sided p) = 0.131- Significance (Two-Sided p) = 0.262A negative correlation indicates an inverse relationship, but it is not statistically significant.#### Paired Samples TestThis test compares the mean difference of errors between the two conditions:- **Mean of Differences = -7.150**- Standard Deviation of Differences = 3.297- Standard Error Mean = 0.737- 95% Confidence Interval of the Difference: Lower = -8.693, Upper = -5.607- **t-value** = -9.698- Degrees of Freedom (df) = 19- Significance: - One-Sided p < 0.001 - Two-Sided p < 0.001The results indicate a highly significant difference in the number of errors, with fewer errors after 8 hours of sleep deprivation compared to 24 hours.#### Paired Samples Effect SizesThis section provides the effect sizes with two metrics:- **Cohen's d**: - Standardizer = 3.297 - Point Estimate = -2.169 - 95% Confidence Interval: Lower = -2.972, Upper = -1.348- **Hedges' correction**: - Standardizer = 3.364 - Point Estimate = -2.125 - 95% Confidence Interval: Lower = -2.913, Upper = -1.321C

Answered: What is Ha? Choice Answers: 1. The…

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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Question

What is H_a?

Choice Answers:

1. The mean of group 1 is not the same as the mean of group 2

2. The mean of group 1 is the same as the mean of group 2

3. The number of errors for 8 hours sleep deprivation is different than the number of errors for 24 hours sleep deprivation

4. The number of errors for 8 hours sleep deprivation is equal to the number of errors for 24 hours sleep deprivation

5. The number of errors for 8 hours sleep deprivation is not different than the number of errors for 24 hours sleep deprivation

6. The number of errors for 8 hours sleep deprivation is not equal to the number of errors for 24 hours sleep deprivation

7. The number of errors for 8 hours sleep deprivation is not the same as the number of errors for 24 hours sleep deprivation

8. The number of errors for 8 hours sleep deprivation is the same as the number of errors for 24 hours sleep deprivation

### Paired Samples Analysis

#### Paired Samples Statistics
This section presents the statistics for errors made after different durations of sleep deprivation:

- **Errors after 8 hours sleep deprivation**:
- Mean = 6.75
- Sample Size (N) = 20
- Standard Deviation = 2.124
- Standard Error Mean = 0.475

- **Errors after 24 hours sleep deprivation**:
- Mean = 13.90
- Sample Size (N) = 20
- Standard Deviation = 2.024
- Standard Error Mean = 0.452

#### Paired Samples Correlations
This analysis shows the correlation between errors after 8 hours and 24 hours of sleep deprivation:

- **Correlation (r) = -0.263**
- Sample Size (N) = 20
- Significance (One-Sided p) = 0.131
- Significance (Two-Sided p) = 0.262

A negative correlation indicates an inverse relationship, but it is not statistically significant.

#### Paired Samples Test
This test compares the mean difference of errors between the two conditions:

- **Mean of Differences = -7.150**
- Standard Deviation of Differences = 3.297
- Standard Error Mean = 0.737
- 95% Confidence Interval of the Difference: Lower = -8.693, Upper = -5.607
- **t-value** = -9.698
- Degrees of Freedom (df) = 19
- Significance:
- One-Sided p < 0.001
- Two-Sided p < 0.001

The results indicate a highly significant difference in the number of errors, with fewer errors after 8 hours of sleep deprivation compared to 24 hours.

#### Paired Samples Effect Sizes
This section provides the effect sizes with two metrics:

- **Cohen's d**:
- Standardizer = 3.297
- Point Estimate = -2.169
- 95% Confidence Interval: Lower = -2.972, Upper = -1.348

- **Hedges' correction**:
- Standardizer = 3.364
- Point Estimate = -2.125
- 95% Confidence Interval: Lower = -2.913, Upper = -1.321

C

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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