Project Instructions:Collect the DataSurvey two different groups of 15 people each. (30 total, 18 years of age or older).Ask one question that requires a numeric answer (interval or ratio).Analyze the DataConduct a t-test: Calculate the mean and standard deviation of both groups, and t.Compare t and the critical value to determine significance.Round decimals to two places past the decimal as they occur. ### Sum of Squares for Two Groups: Table StructureThe table is designed to help calculate the sum of squares for two groups, which is a crucial part of variance and standard deviation calculations in statistics. Here's how the table is structured:#### Group 1- **Columns:** - \( x \): Raw data of Group 1. - \( (x - \bar{x}) \): Deviations from the mean for each data point in Group 1. - \( (x - \bar{x})^2 \): Squared deviations from the mean for Group 1.#### Group 2- **Columns:** - \( x \): Raw data of Group 2. - \( (x - \bar{x}) \): Deviations from the mean for each data point in Group 2. - \( (x - \bar{x})^2 \): Squared deviations from the mean for Group 2.#### Summary Row- This row is for summarizing the calculations: - \( \bar{x} \): Mean of each group. - \( \Sigma \): Sum of squared deviations for each group.### Standard Deviation for SamplesThe formula for the standard deviation (\( s_x \)) of samples is given by:\[s_x = \sqrt{\frac{\Sigma (x - \bar{x})^2}{n-1}}\]Where:- \( \Sigma (x - \bar{x})^2 \) is the sum of squared deviations from the mean.- \( n \) is the number of samples.### t-FormulaThe formula for calculating the t-statistic is shown as:\[t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}\]Where:- \( \bar{x}_1 \) and \( \bar{x}_2 \) are the means of Group 1 and Group 2 respectively.- \( s_1^2 \) and \( s_2^2 \) are the variances of Group 1 and Group 2 respectively.- \( n_1 \) and \( n_2 \) are the number of observations in Group 1 and Group 2.### t-TableA reference link is provided to access the t

Let’s assume that we ask 30 students their weights and their responses are given below: For group 1: 73,70,71,73,68,67,69,72,76,71,72,64,65,63,61For group 2: 63,60,61,63,58,57,59,62,66,61,62,54,55,53,51Using the given formula of t- t= (69-59)/sqrt(18.1429/15 +18.1429/15) =6.43 The critical value of t at 0.05 level of significance and n1+n2-2= 15+15-2= 28 d.f is 2.048. Calculated t> critical t so the result is statistically significant.

Answered: X = X Sx = 5. The t-formula: t = 4.…

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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Project Instructions:

Collect the Data
- Survey two different groups of 15 people each. (30 total, 18 years of age or older).
- Ask one question that requires a numeric answer (interval or ratio).
Analyze the Data
- Conduct a t-test: Calculate the mean and standard deviation of both groups, and t.
- Compare t and the critical value to determine significance.
- Round decimals to two places past the decimal as they occur.