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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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.
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Transcribed Image Text:**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.
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