A market research firm used a sample of individuals to rate the purchase potential of a particular product before and after the individuals saw a new television commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values indicating a higher purchase potential. The null hypothesis stated that the mean rating "after" would be less than or equal to the mean rating "before." Rejection of this hypothesis would show that the commercial improved the mean purchase potential rating. Use ? = 0.05 and the following data to test the hypothesis and comment on the value of the commercial. State the null and alternative hypotheses. (Use ?d = mean rating after − mean rating before.) Calculate the value of the test statistic. (Round your answer to three decimal places.) Calculate the p-value. (Round your answer to four decimal places.)p-value = State your conclusion. **Data Table: Purchase Rating Analysis**This table presents a comparison of purchase ratings for individuals before and after a specific change or intervention. The data outlines ratings for eight individuals, indicating their purchase satisfaction levels.| **Individual** | **Purchase Rating** | |----------------|---------------------| | | **After** | **Before** | | 1 | 6 | 5 | | 2 | 6 | 5 | | 3 | 7 | 8 | | 4 | 4 | 3 | | 5 | 3 | 7 | | 6 | 9 | 8 | | 7 | 7 | 5 | | 8 | 6 | 6 | **Explanation:**- Each row corresponds to a different individual, labeled 1 through 8.- The "After" column shows the purchase rating assigned after the intervention.- The "Before" column displays the purchase rating assigned before the intervention.- Ratings are numeric and indicate the level of satisfaction or approval related to a purchase or service, with higher values suggesting greater satisfaction.**Key Observations:**- For Individuals 1, 2, 4, 6, and 7, there is an increase in satisfaction after the intervention.- Individuals 3 and 5 show a decrease in satisfaction after the intervention.- Individual 8 exhibits no change in their purchase rating.This data is often used in educational settings to teach concepts related to consumer behavior analysis and the impact of interventions on customer satisfaction.

Purchase RatingIndividualAfterBefore165265378443537698775866

Answered: A market research firm used a sample of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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A market research firm used a sample of individuals to rate the purchase potential of a particular product before and after the individuals saw a new television commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values indicating a higher purchase potential. The null hypothesis stated that the mean rating "after" would be less than or equal to the mean rating "before." Rejection of this hypothesis would show that the commercial improved the mean purchase potential rating. Use

? = 0.05 and the following data to test the hypothesis and comment on the value of the commercial.

State the null and alternative hypotheses. (Use ?_d = mean rating after − mean rating before.)

Calculate the value of the test statistic. (Round your answer to three decimal places.)

Calculate the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

**Data Table: Purchase Rating Analysis**

This table presents a comparison of purchase ratings for individuals before and after a specific change or intervention. The data outlines ratings for eight individuals, indicating their purchase satisfaction levels.

| **Individual** | **Purchase Rating** |
|----------------|---------------------|
| | **After** | **Before** |
| 1 | 6 | 5 |
| 2 | 6 | 5 |
| 3 | 7 | 8 |
| 4 | 4 | 3 |
| 5 | 3 | 7 |
| 6 | 9 | 8 |
| 7 | 7 | 5 |
| 8 | 6 | 6 |

**Explanation:**
- Each row corresponds to a different individual, labeled 1 through 8.
- The "After" column shows the purchase rating assigned after the intervention.
- The "Before" column displays the purchase rating assigned before the intervention.
- Ratings are numeric and indicate the level of satisfaction or approval related to a purchase or service, with higher values suggesting greater satisfaction.

**Key Observations:**
- For Individuals 1, 2, 4, 6, and 7, there is an increase in satisfaction after the intervention.
- Individuals 3 and 5 show a decrease in satisfaction after the intervention.
- Individual 8 exhibits no change in their purchase rating.

This data is often used in educational settings to teach concepts related to consumer behavior analysis and the impact of interventions on customer satisfaction.

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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