5) According to the Center for Disease Control, 60.9% of college students nationwide are fully vaccinated for COVID. You wish to determine if the national average describes the mean vaccination rate for college students in San Francisco. You recruit a random sample of 48 college students in San Francisco to test the research question. ### Understanding Statistical Tests: Independent Samples T-test and One Way ANOVA#### Paired Samples T-test Formula:\[ t = \frac{\sum D}{\sqrt{\frac{n(\sum D^2) - (\sum D)^2}{n - 1}}} \]- **n**: Number of pairs of scores (e.g., 8 people measured at two times, df = 8-1 = 7)- **D**: Difference between each pair of scores- \(\sum D\): Sum of the differences- \(\sum D^2\): Sum of the squares of the differences- (\(\sum D\))^2: Sum of the differences squared---#### Independent Samples T-test Formula:\[ t = \frac{\bar{X_1} - \bar{X_2}}{\sqrt{\frac{S_1^2}{n_1-1} + \frac{S_2^2}{n_2-1}}} \]- \(\bar{X_1}\), \(\bar{X_2}\): Means of the first and second groups, respectively- \(S_1^2\), \(S_2^2\): Sample variances of the first and second groups- \(n_1\), \(n_2\): Number of subjects or observations in each group*Note: Calculate the denominator carefully and be aware of whether you're using sample variances or standard deviations.*---#### One Way ANOVA:**Between Groups Sum of Squares (SSB):**1. Subtract the grand mean from each group mean.2. Square the deviation.3. Multiply by n in each group and add the values together.\[ SS_B = \sum n (\bar{X}_i - \bar{X}_g)^2 \]- **n**: Number of subjects or observations in a group- \(\bar{X}_i\): Mean for any group i- \(\bar{X}_g\): Overall or grand mean**Within Groups Sum of Squares (SSW):**1. Subtract each group's mean from the individual scores.2. Add them all up.\[ SS_W = \sum\sum (X - \bar{X}_i)^2 \]- **X**: Any single score within a particular group**ANOVA Table Components:

5) According to the Center for Disease Control, 60.9% of college students nationwide are fully vaccinated for COVID. You wish to determine if the national average describes the mean vaccination rate for college students in San Francisco. You recruit a random sample of 48 college students in San Francisco to test the research question.

5) According to the Center for Disease Control, 60.9% of college students nationwide are fully vaccinated for COVID. You wish to determine if the national average describes the mean vaccination rate for college students in San Francisco. You recruit a random sample of 48 college students in San Francisco to test the research question.

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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