MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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I am unable to obtain the same final answer and wonder if I am calculating a portion incorrectly. Can someone help me break down the continued equation?
![The given image depicts a mathematical equation, specifically a statistical formula used in hypothesis testing. Here is the transcription:
\[
\frac{(149.28 - 212.163) - (0)}{\sqrt{\frac{185.894^2}{853} + \frac{190.58^2}{821}}} = -6.831
\]
Explanation:
This might be an example of computing a test statistic for a hypothesis test, such as a t-test in statistics. Let's break down the components:
1. Numerator: \((149.28 - 212.163) - (0)\)
- This represents the difference between two sample means (149.28 and 212.163), adjusted by the hypothesized difference (0 in this case).
2. Denominator: \(\sqrt{\frac{185.894^2}{853} + \frac{190.58^2}{821}}\)
- This represents the standard error of the difference between the two means.
- \(185.894\) and \(190.58\) are standard deviations of the two samples.
- \(853\) and \(821\) are the sample sizes.
3. The result of the equation is \(-6.831\), which is the value of the test statistic.
This test statistic can then be compared against a critical value from a t-distribution to determine whether to reject the null hypothesis. In this case, the test statistic is \(-6.831\), which would correspond to a very low p-value, indicating strong evidence against the null hypothesis if the p-value falls below a chosen significance level (e.g., 0.05).](https://content.bartleby.com/qna-images/question/bef86afa-6c7a-44b6-8b32-614538bd5c9e/c47f89d4-4072-415c-aaf9-847213b08eae/d0c3qw9_processed.jpeg)
Transcribed Image Text:The given image depicts a mathematical equation, specifically a statistical formula used in hypothesis testing. Here is the transcription:
\[
\frac{(149.28 - 212.163) - (0)}{\sqrt{\frac{185.894^2}{853} + \frac{190.58^2}{821}}} = -6.831
\]
Explanation:
This might be an example of computing a test statistic for a hypothesis test, such as a t-test in statistics. Let's break down the components:
1. Numerator: \((149.28 - 212.163) - (0)\)
- This represents the difference between two sample means (149.28 and 212.163), adjusted by the hypothesized difference (0 in this case).
2. Denominator: \(\sqrt{\frac{185.894^2}{853} + \frac{190.58^2}{821}}\)
- This represents the standard error of the difference between the two means.
- \(185.894\) and \(190.58\) are standard deviations of the two samples.
- \(853\) and \(821\) are the sample sizes.
3. The result of the equation is \(-6.831\), which is the value of the test statistic.
This test statistic can then be compared against a critical value from a t-distribution to determine whether to reject the null hypothesis. In this case, the test statistic is \(-6.831\), which would correspond to a very low p-value, indicating strong evidence against the null hypothesis if the p-value falls below a chosen significance level (e.g., 0.05).
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