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What happens to the confidence intervals when the sample size is increased to 40? (the first sample size was 10)

What happens to the confidence intervals when the sample size is increased to 40? (the first sample size was 10)

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
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  1. What happens to the confidence intervals when the sample size is increased to 40? (the first sample size was 10)
### Fish Length Distribution Analysis #### Overview This visualization represents the distribution of individual fish lengths (measured in millimeters) in a sample. #### Graph Description - **Title Bar:** - **Successes:** 1 - **Failures:** 0 - **Success rate:** 100% - **Button:** "SHOW CALCULATIONS" - **Histogram:** - The X-axis represents the individual fish lengths measured in millimeters (mm), ranging from 0 to 200 mm. - The Y-axis represents the frequency, ranging from 0 to 5. - Gray bars indicate the frequency of fish lengths within specified intervals. - There is a notable distribution peak in the 100 mm length interval. - A horizontal black bar spans above the 100 mm interval, likely representing a confidence interval or statistical summary. - A small orange square is seen at the 100 mm data point, which might signify the mean or a specific data point of interest. - **Text at the bottom of the graph:** - "The true mean is 105." This kind of graph is typically used in statistical analysis to visualize the distribution of data points within a sample set, enabling researchers and students to infer patterns, trends, and statistical measures such as mean values.
Transcribed Image Text:### Fish Length Distribution Analysis #### Overview This visualization represents the distribution of individual fish lengths (measured in millimeters) in a sample. #### Graph Description - **Title Bar:** - **Successes:** 1 - **Failures:** 0 - **Success rate:** 100% - **Button:** "SHOW CALCULATIONS" - **Histogram:** - The X-axis represents the individual fish lengths measured in millimeters (mm), ranging from 0 to 200 mm. - The Y-axis represents the frequency, ranging from 0 to 5. - Gray bars indicate the frequency of fish lengths within specified intervals. - There is a notable distribution peak in the 100 mm length interval. - A horizontal black bar spans above the 100 mm interval, likely representing a confidence interval or statistical summary. - A small orange square is seen at the 100 mm data point, which might signify the mean or a specific data point of interest. - **Text at the bottom of the graph:** - "The true mean is 105." This kind of graph is typically used in statistical analysis to visualize the distribution of data points within a sample set, enabling researchers and students to infer patterns, trends, and statistical measures such as mean values.
**Fish Length Data Analysis** **Overview** - **Successes:** 1 - **Failures:** 0 - **Success Rate:** 100% **Histogram of Individual Fish Lengths** A histogram is displayed at the top of the image, showing the frequency distribution of individual fish lengths measured in millimeters (mm). - The x-axis represents fish length ranging from 0 mm to 200 mm. - The y-axis represents the frequency of fish counts within each length interval. - Most of the fish lengths fall between 60 mm and 140 mm, with a peak in frequency around 100 mm. - A black horizontal line with an attached red square and vertical error bars represents the mean length and the confidence interval (uncertainty) of the measurement. **Confidence Interval Plot** Below the histogram, a confidence interval plot is displayed. - The plot shows multiple sets of confidence intervals centered around different sample means. - Each horizontal line represents a confidence interval for a different sample, illustrating the variability and possible range of the true mean. - The true mean of the fish lengths is indicated to be 105 mm, which is marked by a vertical line at this value. The confidence intervals provide an understanding of the precision of the sample mean estimations and overall variability present in the data. This analysis is important for assessing the statistical significance and reliability of the measurements taken.
Transcribed Image Text:**Fish Length Data Analysis** **Overview** - **Successes:** 1 - **Failures:** 0 - **Success Rate:** 100% **Histogram of Individual Fish Lengths** A histogram is displayed at the top of the image, showing the frequency distribution of individual fish lengths measured in millimeters (mm). - The x-axis represents fish length ranging from 0 mm to 200 mm. - The y-axis represents the frequency of fish counts within each length interval. - Most of the fish lengths fall between 60 mm and 140 mm, with a peak in frequency around 100 mm. - A black horizontal line with an attached red square and vertical error bars represents the mean length and the confidence interval (uncertainty) of the measurement. **Confidence Interval Plot** Below the histogram, a confidence interval plot is displayed. - The plot shows multiple sets of confidence intervals centered around different sample means. - Each horizontal line represents a confidence interval for a different sample, illustrating the variability and possible range of the true mean. - The true mean of the fish lengths is indicated to be 105 mm, which is marked by a vertical line at this value. The confidence intervals provide an understanding of the precision of the sample mean estimations and overall variability present in the data. This analysis is important for assessing the statistical significance and reliability of the measurements taken.
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