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A scientist investigated the effect of cross-fertilization on the heights of plants. In one study, the scientist planted 15 pairs of a species of plant. Each pair consisted of one cross-fertilized plant and one self-fertilized plant grown in the same pot. The table available below gives the height differences, in eighths of an inch, for the 15 pairs. Each difference is obtained by subtracting the height of the self-fertilized plant from that of the cross-fertilized plant. Use the paired t-interval procedure to determine a 99% confidence interval for the difference between the mean heights of cross-fertilized and self-fertilized plants. Interpret the result. (Note: d = 20.13 and sa = 35.80.) Click here to view the data, Click here to viewa table of critical values of t. The 99% confidence interval is from eighths of an inch to eighths of an inch. (Round to two decimal places as needed. Use ascending order.)

A scientist investigated the effect of cross-fertilization on the heights of plants. In one study, the scientist planted 15 pairs of a species of plant. Each pair consisted of one cross-fertilized plant and one self-fertilized plant grown in the same pot. The table available below gives the height differences, in eighths of an inch, for the 15 pairs. Each difference is obtained by subtracting the height of the self-fertilized plant from that of the cross-fertilized plant. Use the paired t-interval procedure to determine a 99% confidence interval for the difference between the mean heights of cross-fertilized and self-fertilized plants. Interpret the result. (Note: d = 20.13 and sa = 35.80.) Click here to view the data, Click here to viewa table of critical values of t. The 99% confidence interval is from eighths of an inch to eighths of an inch. (Round to two decimal places as needed. Use ascending order.)

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter1: Variables, Expressions, And Integers
Section: Chapter Questions
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### The Effect of Cross-Fertilization on Plant Heights #### Study Overview A scientist conducted research to understand the impact of cross-fertilization on the heights of plants. The experiment involved planting 15 pairs of a specific plant species, with each pair consisting of one cross-fertilized plant and one self-fertilized plant grown together in the same pot. The data collected measures the height differences, in eighths of an inch, for these 15 pairs. #### Data Analysis The difference in height for each pair is calculated by subtracting the height of the self-fertilized plant from that of the cross-fertilized plant. To assess the significance of the differences observed, the paired t-interval procedure was used to determine a 99% confidence interval for the mean difference in plant heights between the two groups. **Given Data:** - Mean difference ( \( \bar{d} \) ): 20.13 eighths of an inch - Standard deviation of differences (\( s_{d} \)): 35.80 **Additional Resources:** - Click here to view the data. - Click here to view a table of critical values of t. #### Confidence Interval Calculation The 99% confidence interval for the difference in mean heights is calculated as follows: ``` The 99% confidence interval is from [ ] eighths of an inch to [ ] eighths of an inch. (Round to two decimal places as needed. Use ascending order.) ``` **Note:** Ensure to carry out the calculations and fill in the appropriate values in the confidence interval range. This range will provide the interval within which the true mean difference in plant heights lies with a 99% confidence level. --- This study aims to interpret the results by comparing the interval obtained to zero. If the interval does not contain zero, it suggests a significant difference in heights between cross-fertilized and self-fertilized plants.
Transcribed Image Text:### The Effect of Cross-Fertilization on Plant Heights #### Study Overview A scientist conducted research to understand the impact of cross-fertilization on the heights of plants. The experiment involved planting 15 pairs of a specific plant species, with each pair consisting of one cross-fertilized plant and one self-fertilized plant grown together in the same pot. The data collected measures the height differences, in eighths of an inch, for these 15 pairs. #### Data Analysis The difference in height for each pair is calculated by subtracting the height of the self-fertilized plant from that of the cross-fertilized plant. To assess the significance of the differences observed, the paired t-interval procedure was used to determine a 99% confidence interval for the mean difference in plant heights between the two groups. **Given Data:** - Mean difference ( \( \bar{d} \) ): 20.13 eighths of an inch - Standard deviation of differences (\( s_{d} \)): 35.80 **Additional Resources:** - Click here to view the data. - Click here to view a table of critical values of t. #### Confidence Interval Calculation The 99% confidence interval for the difference in mean heights is calculated as follows: ``` The 99% confidence interval is from [ ] eighths of an inch to [ ] eighths of an inch. (Round to two decimal places as needed. Use ascending order.) ``` **Note:** Ensure to carry out the calculations and fill in the appropriate values in the confidence interval range. This range will provide the interval within which the true mean difference in plant heights lies with a 99% confidence level. --- This study aims to interpret the results by comparing the interval obtained to zero. If the interval does not contain zero, it suggests a significant difference in heights between cross-fertilized and self-fertilized plants.
**Height Differences** The image displays a graphical representation of height differences. The data is arranged in a tabular format with three rows and five columns. Each cell in the table contains a numerical value representing the height differences. The table is structured as follows: | 40 | -63 | 1 | 15 | 8 | |----|-----|----|----|----| | 24 | 20 | 40 | 18 | 29 | | 56 | 27 | 70 | 61 | -44 | Below the table, there are two buttons labeled "Print" and "Done." **Explanation of the Table:** - **Rows:** Each row may represent a different category, group, or time period related to height differences. - **Columns:** Each column may represent a different measurement or data point for these categories. - **Cells:** The values in the cells are the height differences themselves, some of which are positive and some negative. **Usage:** This type of table can be useful for analyzing variations and trends in height measurements across different groups or periods. It could be applicable in educational content related to data analysis, scientific studies on growth, and statistical presentations.
Transcribed Image Text:**Height Differences** The image displays a graphical representation of height differences. The data is arranged in a tabular format with three rows and five columns. Each cell in the table contains a numerical value representing the height differences. The table is structured as follows: | 40 | -63 | 1 | 15 | 8 | |----|-----|----|----|----| | 24 | 20 | 40 | 18 | 29 | | 56 | 27 | 70 | 61 | -44 | Below the table, there are two buttons labeled "Print" and "Done." **Explanation of the Table:** - **Rows:** Each row may represent a different category, group, or time period related to height differences. - **Columns:** Each column may represent a different measurement or data point for these categories. - **Cells:** The values in the cells are the height differences themselves, some of which are positive and some negative. **Usage:** This type of table can be useful for analyzing variations and trends in height measurements across different groups or periods. It could be applicable in educational content related to data analysis, scientific studies on growth, and statistical presentations.
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