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Use at-distribution and the given matched pair sample results to complete the test of the given hypotheses. Assum the results come from random samples, and if the sample sizes are small, assume the underlying distribution of the differences is relatively normal. Assume that differences are computed using d = x1 – x2. Test Ho : Ha O vs Ha : Ha > 0 using the paired data in the following table: Situation 1 120 156 145 175 153 148 180 135 168 157 Situation 2 120 145 142 150 165 148 160 142 162 150

Use at-distribution and the given matched pair sample results to complete the test of the given hypotheses. Assum the results come from random samples, and if the sample sizes are small, assume the underlying distribution of the differences is relatively normal. Assume that differences are computed using d = x1 – x2. Test Ho : Ha O vs Ha : Ha > 0 using the paired data in the following table: Situation 1 120 156 145 175 153 148 180 135 168 157 Situation 2 120 145 142 150 165 148 160 142 162 150

MATLAB: An Introduction with Applications
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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**Statistical Analysis: Understanding Test Statistic and p-Value** In this educational module, you will learn how to interpret a test statistic and a p-value. These two statistical metrics are essential for hypothesis testing. **Instructions:** 1. **Determine the Test Statistic:** - Identify the test statistic value, which in this example is calculated to be 1.48. The test statistic quantifies the difference between observed data and what would be expected under the null hypothesis, expressed as the number of standard deviations. 2. **Calculate the p-Value:** - Here, the p-value is given as 0.914. The p-value indicates the probability of observing the test results assuming that the null hypothesis is true. A smaller p-value suggests stronger evidence against the null hypothesis. **Rounding Rules:** - Ensure that the test statistic is rounded to two decimal places. - The p-value should be rounded to three decimal places. In this example: - The test statistic is rounded to 1.48. - The p-value is rounded to 0.914. By understanding how to interpret these values, you can make informed decisions about hypothesis testing in your research.
Transcribed Image Text:**Statistical Analysis: Understanding Test Statistic and p-Value** In this educational module, you will learn how to interpret a test statistic and a p-value. These two statistical metrics are essential for hypothesis testing. **Instructions:** 1. **Determine the Test Statistic:** - Identify the test statistic value, which in this example is calculated to be 1.48. The test statistic quantifies the difference between observed data and what would be expected under the null hypothesis, expressed as the number of standard deviations. 2. **Calculate the p-Value:** - Here, the p-value is given as 0.914. The p-value indicates the probability of observing the test results assuming that the null hypothesis is true. A smaller p-value suggests stronger evidence against the null hypothesis. **Rounding Rules:** - Ensure that the test statistic is rounded to two decimal places. - The p-value should be rounded to three decimal places. In this example: - The test statistic is rounded to 1.48. - The p-value is rounded to 0.914. By understanding how to interpret these values, you can make informed decisions about hypothesis testing in your research.
**Hypothesis Testing Using Paired Sample t-test** To perform a hypothesis test using a t-distribution with matched pair samples, follow these instructions. Assume the results are derived from random samples. If the sample size is small, consider that the distribution of differences is approximately normal. Calculate differences using the formula \( d = x_1 - x_2 \). **Hypotheses:** - Null Hypothesis (\( H_0 \)): \( \mu_d = 0 \) - Alternative Hypothesis (\( H_a \)): \( \mu_d > 0 \) The data for analysis is provided in the table below: | Situation 1 | Situation 2 | |-------------|-------------| | 120 | 120 | | 156 | 145 | | 145 | 142 | | 175 | 150 | | 153 | 165 | | 148 | 148 | | 180 | 160 | | 135 | 142 | | 168 | 162 | | 157 | 150 | The table shows the data collected under two situations for paired samples. Use this data to calculate the differences, and then perform the t-test to determine if there is a significant difference between the two situations.
Transcribed Image Text:**Hypothesis Testing Using Paired Sample t-test** To perform a hypothesis test using a t-distribution with matched pair samples, follow these instructions. Assume the results are derived from random samples. If the sample size is small, consider that the distribution of differences is approximately normal. Calculate differences using the formula \( d = x_1 - x_2 \). **Hypotheses:** - Null Hypothesis (\( H_0 \)): \( \mu_d = 0 \) - Alternative Hypothesis (\( H_a \)): \( \mu_d > 0 \) The data for analysis is provided in the table below: | Situation 1 | Situation 2 | |-------------|-------------| | 120 | 120 | | 156 | 145 | | 145 | 142 | | 175 | 150 | | 153 | 165 | | 148 | 148 | | 180 | 160 | | 135 | 142 | | 168 | 162 | | 157 | 150 | The table shows the data collected under two situations for paired samples. Use this data to calculate the differences, and then perform the t-test to determine if there is a significant difference between the two situations.
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