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1.3.2 Consider the output given below that was obtained using the One Proportion applet. Use information from the output to find the standardized statistic for a sample propor- tion value of 0.45. Probability of success (n): 0.30 Sample size (n): 25 Number of samples: |1000 | Animate Draw Samples Total = 1000 180 Mean = 0.301 |SD = 0.091 120 60 0.08 0.16 0.24 0.32 0.40 0.48 0.56 0.64 Proportion of success

1.3.2 Consider the output given below that was obtained using the One Proportion applet. Use information from the output to find the standardized statistic for a sample propor- tion value of 0.45. Probability of success (n): 0.30 Sample size (n): 25 Number of samples: |1000 | Animate Draw Samples Total = 1000 180 Mean = 0.301 |SD = 0.091 120 60 0.08 0.16 0.24 0.32 0.40 0.48 0.56 0.64 Proportion of success

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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The image presents two histograms labeled A and B, each displaying the distribution of the proportion of successes. **Histogram A:** - **X-axis:** Proportion of successes ranging from 0.32 to 0.68. - **Y-axis:** Frequency ranging up to 90. - The histogram exhibits a roughly symmetrical bell-shaped distribution centered around 0.50. - **Statistical summary:** - Mean (Average) = 0.502 - Standard Deviation (SD) = 0.049 **Histogram B:** - **X-axis:** Proportion of successes ranging from 0.24 to 0.72. - **Y-axis:** Frequency ranging up to 150. - This histogram also displays a bell-shaped distribution, slightly wider than Histogram A, centered around 0.50. - **Statistical summary:** - Mean (Average) = 0.497 - Standard Deviation (SD) = 0.071 **Interpretation:** Both histograms represent the distribution of proportions of successes, with Histogram B showing a larger spread as indicated by a higher standard deviation, suggesting more variability in the data.
Transcribed Image Text:The image presents two histograms labeled A and B, each displaying the distribution of the proportion of successes. **Histogram A:** - **X-axis:** Proportion of successes ranging from 0.32 to 0.68. - **Y-axis:** Frequency ranging up to 90. - The histogram exhibits a roughly symmetrical bell-shaped distribution centered around 0.50. - **Statistical summary:** - Mean (Average) = 0.502 - Standard Deviation (SD) = 0.049 **Histogram B:** - **X-axis:** Proportion of successes ranging from 0.24 to 0.72. - **Y-axis:** Frequency ranging up to 150. - This histogram also displays a bell-shaped distribution, slightly wider than Histogram A, centered around 0.50. - **Statistical summary:** - Mean (Average) = 0.497 - Standard Deviation (SD) = 0.071 **Interpretation:** Both histograms represent the distribution of proportions of successes, with Histogram B showing a larger spread as indicated by a higher standard deviation, suggesting more variability in the data.
### Understanding the One Proportion Applet Output #### Objective The goal is to interpret the output from the One Proportion applet to find the standardized statistic for a sample proportion value of 0.45. #### Output Details - **Probability of success (π):** 0.30 - **Sample size (n):** 25 - **Number of samples:** 1000 - **Total samples drawn:** 1000 #### Graph Explanation The graph displayed is a histogram showing the distribution of sample proportions. It is a visual representation of how often different proportions of success occur after drawing 1000 samples with the specified parameters. - **Horizontal Axis (x-axis):** Represents the proportion of success, ranging from 0.08 to 0.64. - **Vertical Axis (y-axis):** Represents the frequency (number of occurrences) of each proportion of success. #### Statistical Summary - **Mean:** The average proportion of success calculated from the samples is 0.301. - **Standard Deviation (SD):** The standard deviation of the sample proportions is 0.091, indicating the spread of sample proportions around the mean. #### Applying the Information To find the standardized statistic for a sample proportion value of 0.45, you can use the following formula: \[ z = \frac{\hat{p} - \pi}{SD} \] Where: - \( \hat{p} \) is the sample proportion (0.45) - \( \pi \) is the probability of success (0.30) - \( SD \) is the standard deviation of the sample proportions (0.091) By substituting the values: \[ z = \frac{0.45 - 0.30}{0.091} \] This calculation will provide the standardized statistic (z-score), which helps determine how many standard deviations away the sample proportion 0.45 is from the mean proportion 0.301.
Transcribed Image Text:### Understanding the One Proportion Applet Output #### Objective The goal is to interpret the output from the One Proportion applet to find the standardized statistic for a sample proportion value of 0.45. #### Output Details - **Probability of success (π):** 0.30 - **Sample size (n):** 25 - **Number of samples:** 1000 - **Total samples drawn:** 1000 #### Graph Explanation The graph displayed is a histogram showing the distribution of sample proportions. It is a visual representation of how often different proportions of success occur after drawing 1000 samples with the specified parameters. - **Horizontal Axis (x-axis):** Represents the proportion of success, ranging from 0.08 to 0.64. - **Vertical Axis (y-axis):** Represents the frequency (number of occurrences) of each proportion of success. #### Statistical Summary - **Mean:** The average proportion of success calculated from the samples is 0.301. - **Standard Deviation (SD):** The standard deviation of the sample proportions is 0.091, indicating the spread of sample proportions around the mean. #### Applying the Information To find the standardized statistic for a sample proportion value of 0.45, you can use the following formula: \[ z = \frac{\hat{p} - \pi}{SD} \] Where: - \( \hat{p} \) is the sample proportion (0.45) - \( \pi \) is the probability of success (0.30) - \( SD \) is the standard deviation of the sample proportions (0.091) By substituting the values: \[ z = \frac{0.45 - 0.30}{0.091} \] This calculation will provide the standardized statistic (z-score), which helps determine how many standard deviations away the sample proportion 0.45 is from the mean proportion 0.301.
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