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What is the p value and 95 confidence intervals based on the picture?

What is the p value and 95 confidence intervals based on the picture?

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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What is the p value and 95 confidence intervals based on the picture?
The image shows a histogram titled "Figure 2: Randomization Test for a difference in mean." The histogram represents a normal distribution with clearly marked sections for the left tail, right tail, and the central part of the distribution. Key details include: - **Two-Tail Test**: The graph highlights that a two-tail test is conducted, with emphasis on measuring significance at both extremes of the distribution. - **Histogram Details**: - The central part of the distribution is shown in black and represents 95% of the confidence interval, indicated by the label "0.950." - The tails are marked in red, with each tail area representing 2.5% of the distribution (labeled "0.025" on either side). - Tail values are marked at -17.025 for the left tail and 16.789 for the right tail, suggesting the cut-off points for significance. - **Statistics**: - **Samples**: 5000 - **Mean**: -0.233 - **Standard Error**: 8.556 - **Bottom Description**: - The textual excerpt explains that since the data follows a normal distribution, a two-tail test is run with a 95% confidence interval. It references an original sample statistic (\(\overline{x_1} - \overline{x_2} = 21.79\)) which may be related to interpreting test results against the threshold values. This visualization aids in understanding how randomization tests are used to determine significant differences between means in a statistical sample, focusing on the tails of the distribution to assess significance.
Transcribed Image Text:The image shows a histogram titled "Figure 2: Randomization Test for a difference in mean." The histogram represents a normal distribution with clearly marked sections for the left tail, right tail, and the central part of the distribution. Key details include: - **Two-Tail Test**: The graph highlights that a two-tail test is conducted, with emphasis on measuring significance at both extremes of the distribution. - **Histogram Details**: - The central part of the distribution is shown in black and represents 95% of the confidence interval, indicated by the label "0.950." - The tails are marked in red, with each tail area representing 2.5% of the distribution (labeled "0.025" on either side). - Tail values are marked at -17.025 for the left tail and 16.789 for the right tail, suggesting the cut-off points for significance. - **Statistics**: - **Samples**: 5000 - **Mean**: -0.233 - **Standard Error**: 8.556 - **Bottom Description**: - The textual excerpt explains that since the data follows a normal distribution, a two-tail test is run with a 95% confidence interval. It references an original sample statistic (\(\overline{x_1} - \overline{x_2} = 21.79\)) which may be related to interpreting test results against the threshold values. This visualization aids in understanding how randomization tests are used to determine significant differences between means in a statistical sample, focusing on the tails of the distribution to assess significance.
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