MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Concept explainers

Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
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I need help with this question for parts b-d
**Comparison of Average Sunday Church Donations: Presbyterians vs. Catholics** *Research Question:* Does the average Presbyterian donate more than the average Catholic in church on Sundays? *Study Details:* - **Presbyterian Donations:** - Sample Size: 56 members - Average Donation: $21 - Standard Deviation: $5 - **Catholic Donations:** - Sample Size: 46 members - Average Donation: $16 - Standard Deviation: $15 *Analysis at α = 0.01 Level of Significance:* 1. **Statistical Test Selection:** - For this study, we need to use a **two-sample t-test**. 2. **Hypotheses:** - **Null Hypothesis (H₀):** - μ₁ ≤ μ₂ (The mean donation by Presbyterians is less than or equal to the mean donation by Catholics) - **Alternative Hypothesis (H₁):** - μ₁ > μ₂ (The mean donation by Presbyterians is greater than the mean donation by Catholics) 3. **Test Statistic Calculation:** - The test statistic is calculated using the given sample sizes, means, and standard deviations. 4. **P-value Determination:** - The **p-value** is obtained from the t-distribution table or by using statistical software. 5. **Comparison Decision:** - **Compare the p-value with α (0.01):** - If the p-value is less than 0.01, we reject the null hypothesis (indicating significant evidence). - If the p-value is greater than 0.01, we do not reject the null hypothesis (indicating insufficient evidence). 6. **Conclusion:** - Based on the p-value and the test statistic, conclude if there is significant evidence to state that Presbyterians donate more on average than Catholics. *How to Interpret the Results:* - If results are **statistically significant** at α = 0.01: - We have sufficient evidence to conclude that the population mean amount of money that Presbyterians donate is more than the population mean amount of money that Catholics donate. - If results are **statistically insignificant** at α = 0.01: - There is insufficient evidence to conclude that the population mean amount of money that Presbyterians donate is more than the population mean amount of
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Transcribed Image Text:**Comparison of Average Sunday Church Donations: Presbyterians vs. Catholics** *Research Question:* Does the average Presbyterian donate more than the average Catholic in church on Sundays? *Study Details:* - **Presbyterian Donations:** - Sample Size: 56 members - Average Donation: $21 - Standard Deviation: $5 - **Catholic Donations:** - Sample Size: 46 members - Average Donation: $16 - Standard Deviation: $15 *Analysis at α = 0.01 Level of Significance:* 1. **Statistical Test Selection:** - For this study, we need to use a **two-sample t-test**. 2. **Hypotheses:** - **Null Hypothesis (H₀):** - μ₁ ≤ μ₂ (The mean donation by Presbyterians is less than or equal to the mean donation by Catholics) - **Alternative Hypothesis (H₁):** - μ₁ > μ₂ (The mean donation by Presbyterians is greater than the mean donation by Catholics) 3. **Test Statistic Calculation:** - The test statistic is calculated using the given sample sizes, means, and standard deviations. 4. **P-value Determination:** - The **p-value** is obtained from the t-distribution table or by using statistical software. 5. **Comparison Decision:** - **Compare the p-value with α (0.01):** - If the p-value is less than 0.01, we reject the null hypothesis (indicating significant evidence). - If the p-value is greater than 0.01, we do not reject the null hypothesis (indicating insufficient evidence). 6. **Conclusion:** - Based on the p-value and the test statistic, conclude if there is significant evidence to state that Presbyterians donate more on average than Catholics. *How to Interpret the Results:* - If results are **statistically significant** at α = 0.01: - We have sufficient evidence to conclude that the population mean amount of money that Presbyterians donate is more than the population mean amount of money that Catholics donate. - If results are **statistically insignificant** at α = 0.01: - There is insufficient evidence to conclude that the population mean amount of money that Presbyterians donate is more than the population mean amount of
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