Find the test statisticFind critical value Is there sufficient evidence to conclude that there is a difference in the mean rating of the pens following exposure to five advertisements? Is there significant evidence that Ad A and Ad B differ in mean ratings?Is there significant evidence that Ad A and Ad C differ in mean ratings?Is there significant evidence that Ad A and Ad D differ in mean ratings?Is there significant evidence that Ad A and Ad E differ in mean ratings?Is there significant evidence that Ad B and Ad C differ in mean ratings?Is there significant evidence that Ad B and Ad D differ in mean ratings?Is there significant evidence that Ad B and Ad E differ in mean ratings?Is there significant evidence that Ad C and Ad D differ in mean ratings?Is there significant evidence that Ad C and Ad E differ in mean ratings?Is there significant evidence that Ad D and Ad E differ in mean ratings?At the 0.01 level of significance, is there evidence of a difference in the variation in ratings among the five advertisements? Determine the hypothesis. Determine test statistic and critical value for that. Determine if there is sufficient evidence for that. Which ad should you use and why? **Advertising Scores**This table represents the combined scores from three ratings for five different advertisements, labeled A through E. Each column corresponds to an advertisement and contains scores for various assessments.| | A | B | C | D | E ||---|---|---|---|---|---|| 1 | 14 | 17 | 10 | 4 | 14 || 2 | 20 | 16 | 8 | 5 | 17 || 3 | 17 | 21 | 11 | 14 | 16 || 4 | 19 | 21 | 15 | 10 | 12 || 5 | 21 | 21 | 13 | 9 | 16 || 6 | 20 | 18 | 15 | 10 | 16 |### Explanation:Each row in the table represents a different evaluation instance.- Columns labeled A to E show the scores for each advertisement across six different evaluations. - The numbers represent the total scores given to each advertisement in each evaluation session. These scores are presumably summed from different criteria ratings to provide an overall assessment of the effectiveness or appeal of each advertisement. This table can be used to analyze trends, such as which advertisements consistently score higher or lower, and can be further explored for insights into advertisement effectiveness. ### Experiment OverviewAn experiment was conducted to compare five different advertisements for a pen:- **Advertisement A**: Greatly undersells the pen.- **Advertisement B**: Slightly undersells the pen.- **Advertisement C**: Slightly oversells the pen.- **Advertisement D**: Greatly oversells the pen.- **Advertisement E**: Accurately states the pen’s qualities.A sample of 30 adult respondents was randomly assigned to these five advertisements. After viewing an advertisement, each respondent rated the pen from 1 to 7 (1 representing the lowest score and 7 the highest) based on three characteristics. This process provided combined scores from the three ratings by the 30 respondents, summarized in a data table.### Hypothesis TestingThe goal is to determine whether there is a significant difference in the mean ratings of the pens after exposure to the five different advertisements at a 0.01 significance level.#### Hypotheses- **Option A**: - Null hypothesis (H₀): μ₁ = μ₂ = ... = μ₅ - Alternative hypothesis (H₁): μ₁ ≠ μ₂ ≠ ... ≠ μ₅- **Option B**: - Null hypothesis (H₀): μ₁ = μ₂ = ... = μ₆ - Alternative hypothesis (H₁): Not all the means are equal.- **Option C**: - Null hypothesis (H₀): μ₁ ≠ μ₂ ≠ ... ≠ μ₆ - Alternative hypothesis (H₁): Not all the means are equal.- **Option D** (Correct Choice): - Null hypothesis (H₀): μ₁ = μ₂ = ... = μ₅ - Alternative hypothesis (H₁): Not all the means are equal.### Data AnalysisTo proceed with the hypothesis testing, you need to calculate the test statistic using the F-statistic formula. Enter the calculated F_STAT value in the provided field, rounding it to two decimal places as required.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Find the test statistic Find critical value Is there sufficient evidence to conclude that there is a difference in the mean rating of the pens following exposure to five advertisements? Is there significant evidence that Ad A and Ad B differ in mean ratings? Is there significant evidence that Ad A and Ad C differ in mean ratings? Is there significant evidence that Ad A and Ad D differ in mean ratings? Is there significant evidence that Ad A and Ad E differ in mean ratings? Is there significant evidence that Ad B and Ad C differ in mean ratings? Is there significant evidence that Ad B and Ad D differ in mean ratings? Is there significant evidence that Ad B and Ad E differ in mean ratings? Is there significant evidence that Ad C and Ad D differ in mean ratings? Is there significant evidence that Ad C and Ad E differ in mean ratings? Is there significant evidence that Ad D and Ad E differ in mean ratings? At the 0.01 level of significance, is there evidence of a difference in the variation in ratings among the five advertisements? Determine the hypothesis. Determine test statistic and critical value for that. Determine if there is sufficient evidence for that. Which ad should you use and why?

**Advertising Scores**

This table represents the combined scores from three ratings for five different advertisements, labeled A through E. Each column corresponds to an advertisement and contains scores for various assessments.

| | A | B | C | D | E |
|---|---|---|---|---|---|
| 1 | 14 | 17 | 10 | 4 | 14 |
| 2 | 20 | 16 | 8 | 5 | 17 |
| 3 | 17 | 21 | 11 | 14 | 16 |
| 4 | 19 | 21 | 15 | 10 | 12 |
| 5 | 21 | 21 | 13 | 9 | 16 |
| 6 | 20 | 18 | 15 | 10 | 16 |

### Explanation:
Each row in the table represents a different evaluation instance.
- Columns labeled A to E show the scores for each advertisement across six different evaluations.
- The numbers represent the total scores given to each advertisement in each evaluation session. These scores are presumably summed from different criteria ratings to provide an overall assessment of the effectiveness or appeal of each advertisement.

This table can be used to analyze trends, such as which advertisements consistently score higher or lower, and can be further explored for insights into advertisement effectiveness.

### Experiment Overview

An experiment was conducted to compare five different advertisements for a pen:
- **Advertisement A**: Greatly undersells the pen.
- **Advertisement B**: Slightly undersells the pen.
- **Advertisement C**: Slightly oversells the pen.
- **Advertisement D**: Greatly oversells the pen.
- **Advertisement E**: Accurately states the pen’s qualities.

A sample of 30 adult respondents was randomly assigned to these five advertisements. After viewing an advertisement, each respondent rated the pen from 1 to 7 (1 representing the lowest score and 7 the highest) based on three characteristics. This process provided combined scores from the three ratings by the 30 respondents, summarized in a data table.

### Hypothesis Testing

The goal is to determine whether there is a significant difference in the mean ratings of the pens after exposure to the five different advertisements at a 0.01 significance level.

#### Hypotheses

- **Option A**:
- Null hypothesis (H₀): μ₁ = μ₂ = ... = μ₅
- Alternative hypothesis (H₁): μ₁ ≠ μ₂ ≠ ... ≠ μ₅

- **Option B**:
- Null hypothesis (H₀): μ₁ = μ₂ = ... = μ₆
- Alternative hypothesis (H₁): Not all the means are equal.

- **Option C**:
- Null hypothesis (H₀): μ₁ ≠ μ₂ ≠ ... ≠ μ₆
- Alternative hypothesis (H₁): Not all the means are equal.

- **Option D** (Correct Choice):
- Null hypothesis (H₀): μ₁ = μ₂ = ... = μ₅
- Alternative hypothesis (H₁): Not all the means are equal.

### Data Analysis

To proceed with the hypothesis testing, you need to calculate the test statistic using the F-statistic formula. Enter the calculated F_STAT value in the provided field, rounding it to two decimal places as required.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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