How is the confidence interval and the point estimate for the population mean visually shown?How was a confidence interval that did NOT capture the population mean visually shown? How often would we expect this to occur? On this educational website, the results of a fish length measurement study are displayed graphically. The header of the page summarizes the success metrics:- **Successes:** 1- **Failures:** 0- **Success rate:** 100%The main content features a histogram titled "Individual fish length (mm)", which visualizes the distribution of lengths of individual fish within the sample.### Histogram Details:- **X-axis:** Represents the length of individual fish in millimeters (mm), ranging from 0 mm to 200 mm.- **Y-axis:** Represents the frequency, ranging from 0 to 5, indicating how many fish fall into each length category.- The histogram shows several vertical bars of varying heights, each bar representing a length interval. - 40 mm to 60 mm: Frequency of 1 - 60 mm to 80 mm: Frequency of 2 - 80 mm to 100 mm: Frequency of 1 - 100 mm to 120 mm: Frequency of 1 - 120 mm to 140 mm: Frequency of 4 - 140 mm to 160 mm: Frequency of 1 - 160 mm onwards: Frequency of 0- Additionally, there is a horizontal black line with a small orange square in the middle. This line likely represents a statistical measure of central tendency, such as the mean or median, and the square could denote a specific value like the mean fish length.A button labeled **"SHOW CALCULATIONS"** is provided, suggesting that users can click it to view the detailed statistical calculations behind the histogram.This graphical representation and the accompanying metrics provide insights into the distribution and central values of the individual fish lengths in the study. ### Fish Length Analysis and Success Rates**Overview:**- **Successes:** 24- **Failures:** 1- **Success Rate:** 96.0% **Graphical Analysis:** 1. **Histogram of Individual Fish Length:** - This histogram displays the distribution of fish lengths measured in millimeters (mm). - The x-axis represents the fish lengths ranging from 0 to 200 mm. - The y-axis shows the frequency (number of occurrences) of each length interval. - From the histogram, the lengths are clustered around the following intervals with varying frequencies: - 60-80 mm: 2 occurrences - 80-100 mm: 3 occurrences - 100-120 mm: 4 occurrences - 120-140 mm: 3 occurrences 2. **Error Bar Plot:** - This plot showcases individual data points with their corresponding confidence intervals. - The horizontal red line at the top represents a reference or a measured value. - Each data point is marked by an orange square and accompanied by a horizontal black line symbolizing the confidence interval for that measurement. - The vertical grey line signifies the true mean value of 105 mm, indicating the average fish length. **Conclusion:**This analysis provides insights into the length variability of individual fish and displays a high success rate in data collection, with 24 successful measurements against a single failure. The true mean length of 105 mm can be used for further biological or ecological inferences.

The objective is to infer the confidence intervals and the point estimate for the true mean.

Answered: 50 4 3 2 1 0 Successes: 24 40 0 20…

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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100%

How is the confidence interval and the point estimate for the population mean visually shown?
How was a confidence interval that did NOT capture the population mean visually shown? How often would we expect this to occur?

On this educational website, the results of a fish length measurement study are displayed graphically. The header of the page summarizes the success metrics:
- **Successes:** 1
- **Failures:** 0
- **Success rate:** 100%

The main content features a histogram titled "Individual fish length (mm)", which visualizes the distribution of lengths of individual fish within the sample.

### Histogram Details:
- **X-axis:** Represents the length of individual fish in millimeters (mm), ranging from 0 mm to 200 mm.
- **Y-axis:** Represents the frequency, ranging from 0 to 5, indicating how many fish fall into each length category.
- The histogram shows several vertical bars of varying heights, each bar representing a length interval.
- 40 mm to 60 mm: Frequency of 1
- 60 mm to 80 mm: Frequency of 2
- 80 mm to 100 mm: Frequency of 1
- 100 mm to 120 mm: Frequency of 1
- 120 mm to 140 mm: Frequency of 4
- 140 mm to 160 mm: Frequency of 1
- 160 mm onwards: Frequency of 0

- Additionally, there is a horizontal black line with a small orange square in the middle. This line likely represents a statistical measure of central tendency, such as the mean or median, and the square could denote a specific value like the mean fish length.

A button labeled **"SHOW CALCULATIONS"** is provided, suggesting that users can click it to view the detailed statistical calculations behind the histogram.

This graphical representation and the accompanying metrics provide insights into the distribution and central values of the individual fish lengths in the study.

### Fish Length Analysis and Success Rates

**Overview:**
- **Successes:** 24
- **Failures:** 1
- **Success Rate:** 96.0%

**Graphical Analysis:**

1. **Histogram of Individual Fish Length:**
- This histogram displays the distribution of fish lengths measured in millimeters (mm).
- The x-axis represents the fish lengths ranging from 0 to 200 mm.
- The y-axis shows the frequency (number of occurrences) of each length interval.
- From the histogram, the lengths are clustered around the following intervals with varying frequencies:
- 60-80 mm: 2 occurrences
- 80-100 mm: 3 occurrences
- 100-120 mm: 4 occurrences
- 120-140 mm: 3 occurrences

2. **Error Bar Plot:**
- This plot showcases individual data points with their corresponding confidence intervals.
- The horizontal red line at the top represents a reference or a measured value.
- Each data point is marked by an orange square and accompanied by a horizontal black line symbolizing the confidence interval for that measurement.
- The vertical grey line signifies the true mean value of 105 mm, indicating the average fish length.

**Conclusion:**
This analysis provides insights into the length variability of individual fish and displays a high success rate in data collection, with 24 successful measurements against a single failure. The true mean length of 105 mm can be used for further biological or ecological inferences.

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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