**Data Set Analysis**Use the following data set: **40, 33, 77, 12, 23, 56, 23, 19, 29** (in minutes). Assume the data is approximately bell-shaped and is a sample.In this dataset, each number represents a time duration recorded in minutes. The assumption that the data is "approximately bell-shaped" suggests that it follows a normal distribution, which is typically symmetrical, with most data points clustering around the mean. This characteristic is useful for statistical analysis, helping to apply techniques like z-scores and standard deviation. Understanding the shape of the data can assist in deriving insights about the average performance and variability within this sample. **Hypothesis Testing for Mean (\( \mu \))****Objective:** - Test the claim that the population mean (\( \mu \)) is equal to 15.- Sketch the distribution indicating the Critical Value.- Evaluate the Test Statistic.- Provide the p-value.**Steps:**1. **State the Hypotheses:** - Null Hypothesis (\( H_0 \)): \( \mu = 15 \) - Alternative Hypothesis (\( H_a \)): \( \mu \neq 15 \)2. **Select the Significance Level (\( \alpha \)):** - Common choices for \( \alpha \) are 0.05, 0.01, etc.3. **Sketch the Distribution:** - Draw a normal distribution curve. - Mark the Critical Value(s) on the curve. - The Critical Value delimiters will depend on your significance level.4. **Calculate the Test Statistic:** - Use the formula for the test statistic (e.g., Z or T) based on the sample data. - Plug in your sample mean, population mean, standard deviation, and sample size into the formula.5. **Determine the p-value:** - Locate the Test Statistic on the standard normal distribution. - The p-value is the probability that the test statistic is as extreme as, or more extreme than, the observed value under the null hypothesis.6. **Make a Decision:** - If the p-value < \( \alpha \), reject the null hypothesis (\( H_0 \)). - If the p-value ≥ \( \alpha \), do not reject the null hypothesis (\( H_0 \)).**Conclusion:**- Based on the results, conclude whether there is sufficient evidence to reject the claim that \( \mu = 15 \).**Visual Explanation:**- A graphical representation can help visualize where the test statistic and critical values lie in relation to the significance level on the curve.

Name: **Data Set Analysis**Use the following data set: **40, 33, 77, 12, 23
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Description: **Data Set Analysis**Use the following data set: **40, 33, 77, 12, 23, 56, 23, 19, 29** (in minutes). Assume the data is approximately bell-shaped and is a sample.In this dataset, each number represents a time duration recorded in minutes. The assum

Given data: 40, 33, 77, 12, 23, 56, 23, 19, 29. To test the claim that μ=15. State the Hypothesis…

Answered: f) Test the claim that µ = 15. Provide…

Math

Statistics

f) Test the claim that µ = 15. Provide a sketch of the Critical Value. Evaluate the Test Statistic and provide the p- value.

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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