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There is a new fertilizer that is supposed to increase plant growth. To test this, 16 soy bean plants were treated with the fertilizer and grown for 3 weeks in a controlled environment. The mean height was determine to be 24 in. with a standard deviation of 8 in. When grown under the same conc ns, typical soy bean plant= are expected to grow an average height of 20 inches after 3 weeks. Was there an effect of the fertilizer on plant height? (3 points) A) Which test would you choose to answer this question? Be specific. (0.5) B) State null and alternative hypotheses as both verbal and mathematical statements. (1)

There is a new fertilizer that is supposed to increase plant growth. To test this, 16 soy bean plants were treated with the fertilizer and grown for 3 weeks in a controlled environment. The mean height was determine to be 24 in. with a standard deviation of 8 in. When grown under the same conc ns, typical soy bean plant= are expected to grow an average height of 20 inches after 3 weeks. Was there an effect of the fertilizer on plant height? (3 points) A) Which test would you choose to answer this question? Be specific. (0.5) B) State null and alternative hypotheses as both verbal and mathematical statements. (1)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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**Analysis of Fertilizer's Effect on Plant Height: Educational Activity** **Scenario:** A new fertilizer is purported to enhance plant growth. To evaluate this, 16 soybean plants were treated with the fertilizer and grown for 3 weeks in a controlled environment. The mean height was measured to be 24 inches, with a standard deviation of 8 inches. Typically, without fertilizer, soybean plants grown under the same conditions reach an average height of 20 inches after 3 weeks. **Research Question:** Was there an effect of the fertilizer on plant height? (3 points) **Tasks:** A) **Choose a Test:** Identify the appropriate statistical test to determine the effect, providing a specific rationale. (0.5) B) **Formulate Hypotheses:** State the null and alternative hypotheses both verbally and mathematically. (1) C) **Determine Critical Value:** For a Type I error rate (α) of 0.05, specify the critical value used for this test. (0.5) D) **Decision Rule:** Should the computed test statistic be greater or less than the critical value to reject the null hypothesis? (0.5) E) **Interpret Test Statistic:** If the computed test statistic was 2.0, what conclusion would you draw? (0.5) **Solution:** A) Use the t-test, as the sample size is limited, or smaller, and the variance is unknown. B) **Hypotheses:** - Null hypothesis (H0): The fertilizer has no effect on plant height. - Alternative hypothesis (H1): The fertilizer increases plant height. C) For a Type I error rate of 0.05, look up the critical t-value for 15 degrees of freedom (n-1 = 16-1). This is approximately 2.131 for a one-tailed test. D) In order to reject the null hypothesis, the computed test statistic should be greater than the critical value. E) If the computed test statistic was 2.0, the conclusion would be that there isn't enough evidence to reject the null hypothesis at the 0.05 significance level.
Transcribed Image Text:**Analysis of Fertilizer's Effect on Plant Height: Educational Activity** **Scenario:** A new fertilizer is purported to enhance plant growth. To evaluate this, 16 soybean plants were treated with the fertilizer and grown for 3 weeks in a controlled environment. The mean height was measured to be 24 inches, with a standard deviation of 8 inches. Typically, without fertilizer, soybean plants grown under the same conditions reach an average height of 20 inches after 3 weeks. **Research Question:** Was there an effect of the fertilizer on plant height? (3 points) **Tasks:** A) **Choose a Test:** Identify the appropriate statistical test to determine the effect, providing a specific rationale. (0.5) B) **Formulate Hypotheses:** State the null and alternative hypotheses both verbally and mathematically. (1) C) **Determine Critical Value:** For a Type I error rate (α) of 0.05, specify the critical value used for this test. (0.5) D) **Decision Rule:** Should the computed test statistic be greater or less than the critical value to reject the null hypothesis? (0.5) E) **Interpret Test Statistic:** If the computed test statistic was 2.0, what conclusion would you draw? (0.5) **Solution:** A) Use the t-test, as the sample size is limited, or smaller, and the variance is unknown. B) **Hypotheses:** - Null hypothesis (H0): The fertilizer has no effect on plant height. - Alternative hypothesis (H1): The fertilizer increases plant height. C) For a Type I error rate of 0.05, look up the critical t-value for 15 degrees of freedom (n-1 = 16-1). This is approximately 2.131 for a one-tailed test. D) In order to reject the null hypothesis, the computed test statistic should be greater than the critical value. E) If the computed test statistic was 2.0, the conclusion would be that there isn't enough evidence to reject the null hypothesis at the 0.05 significance level.
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