Researchers conducted trials to investigate the effects of color on creativity. Subjects with a. Red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given in the accompanying table. Higher scores correspond to more creativity. The researchers make the claim that "blue enhances performance on a creative task". Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. what are the null and alternative hypothesis identify the test statistic ifentify the p value **Study Summary Statistics**A study was conducted to investigate the effects of color on creativity. Independent simple random samples were drawn for two background colors: blue and red. The creativity scores of subjects exposed to these colors were evaluated.The results of the study are summarized in the table below:| Background | \( \mu \) | \( n \) | \( \bar{x} \) | \( s \) ||------------|-----------|---------|---------------|----------|| Blue | \( \mu_1 \) | 41 | 3.73 | 0.56 || Red | \( \mu_2 \) | 34 | 2.82 | 0.86 |**Explanation of Terms:**- \( \mu \): Population mean (hypothetical)- \( n \): Sample size- \( \bar{x} \): Sample mean score for creativity- \( s \): Standard deviation of the sampleIn this data, the blue background had a larger sample size and higher average creativity score than the red background. The standard deviation was lower for the blue background, indicating less variability in creativity scores among subjects exposed to the blue background.

Given Data : For Sample 1 x̄1 = 3.73 s1 = 0.56 n1 = 41 For Sample 2…

Answered: Researchers conducted trials to…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Researchers conducted trials to investigate the effects of color on creativity. Subjects with a. Red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given in the accompanying table. Higher scores correspond to more creativity. The researchers make the claim that "blue enhances performance on a creative task". Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal.
what are the null and alternative hypothesis

identify the test statistic

ifentify the p value

**Study Summary Statistics**

A study was conducted to investigate the effects of color on creativity. Independent simple random samples were drawn for two background colors: blue and red. The creativity scores of subjects exposed to these colors were evaluated.

The results of the study are summarized in the table below:

| Background | \( \mu \) | \( n \) | \( \bar{x} \) | \( s \) |
|------------|-----------|---------|---------------|----------|
| Blue | \( \mu_1 \) | 41 | 3.73 | 0.56 |
| Red | \( \mu_2 \) | 34 | 2.82 | 0.86 |

**Explanation of Terms:**

- \( \mu \): Population mean (hypothetical)
- \( n \): Sample size
- \( \bar{x} \): Sample mean score for creativity
- \( s \): Standard deviation of the sample

In this data, the blue background had a larger sample size and higher average creativity score than the red background. The standard deviation was lower for the blue background, indicating less variability in creativity scores among subjects exposed to the blue background.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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