MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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A paint manufacturer wishes to compare the drying times of two different types of paint. Independent random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times (in hours) were recorded. The summary statistics are given in the image below. Use a 0.01 significance level to test the claim that the
Transcribed Image Text:### Statistical Comparison of Type A and Type B
The table below presents a comparison of two types, namely Type A and Type B, based on their respective means, standard deviations, and sample sizes.
| | Type A | Type B |
|----------|----------|----------|
| Mean (\(\bar{x}\)) | 76.9 | 66.3 |
| Standard Deviation (\(s\)) | 4.5 | 5.1 |
| Sample Size (\(n\))| 11 | 9 |
#### Detailed Explanation:
- **Mean (\(\bar{x}\))**: This represents the average value for each type.
- Type A: The mean value is 76.9.
- Type B: The mean value is 66.3.
- **Standard Deviation (\(s\))**: This measures the amount of variation or dispersion from the mean.
- Type A: The standard deviation is 4.5, indicating less variability around the mean compared to Type B.
- Type B: The standard deviation is 5.1, indicating more variability around the mean compared to Type A.
- **Sample Size (\(n\))**: This denotes the number of observations in each sample.
- Type A: The sample size is 11.
- Type B: The sample size is 9.
The data provided can be used for various statistical analyses such as hypothesis testing, confidence interval calculations, or comparative studies to determine significant differences between Type A and Type B.
Transcribed Image Text:**Linear Correlation**
### Critical Values and Statistical Significance
*If \( |r| > CV \), then correlation is statistically significant.*
<table>
<tr>
<th>n</th>
<th>Critical Value (CV)</th>
</tr>
<tr>
<td>4</td>
<td>.950</td>
</tr>
<tr>
<td>5</td>
<td>.878</td>
</tr>
<tr>
<td>6</td>
<td>.811</td>
</tr>
<tr>
<td>7</td>
<td>.754</td>
</tr>
<tr>
<td>8</td>
<td>.707</td>
</tr>
<tr>
<td>9</td>
<td>.666</td>
</tr>
<tr>
<td>10</td>
<td>.632</td>
</tr>
<tr>
<td>11</td>
<td>.602</td>
</tr>
<tr>
<td>12</td>
<td>.576</td>
</tr>
<tr>
<td>13</td>
<td>.553</td>
</tr>
<tr>
<td>14</td>
<td>.532</td>
</tr>
<tr>
<td>15</td>
<td>.514</td>
</tr>
</table>
This table lists the critical values (CV) for a linear correlation when considering different sample sizes (n). When the absolute value of the correlation coefficient \( |r| \) exceeds the critical value (CV) corresponding to the sample size, the correlation is deemed statistically significant.
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