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The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient is 36 centimeters. To check whether this is still accurate, heights are measured for a random sample of 18 Begonias grown while being treated with the nutrient. The sample mean and sample standard deviation of those height measurements are 40 centimeters and 7 centimeters, respectively. 圖 Assume that the heights of treated Begonias are approximately normally distributed. Based on the sample, can it be concluded that the population mean height of treated begonias, µ, is different from that reported in the journal? Use the 0.10 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) |(a) State the null hypothesis Ho and the alternative hypothesis H,. Ho : 0 H : 0 |(b) Determine the type of test statistic to use. O=0 OSO |(c) Find the value of the test statistic. (Round to three or more decimal places.) O

The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient is 36 centimeters. To check whether this is still accurate, heights are measured for a random sample of 18 Begonias grown while being treated with the nutrient. The sample mean and sample standard deviation of those height measurements are 40 centimeters and 7 centimeters, respectively. 圖 Assume that the heights of treated Begonias are approximately normally distributed. Based on the sample, can it be concluded that the population mean height of treated begonias, µ, is different from that reported in the journal? Use the 0.10 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) |(a) State the null hypothesis Ho and the alternative hypothesis H,. Ho : 0 H : 0 |(b) Determine the type of test statistic to use. O=0 OSO |(c) Find the value of the test statistic. (Round to three or more decimal places.) O

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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**Title: Two-Tailed Hypothesis Testing for Mean Height of Begonias** The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient is 36 centimeters. To check whether this is still accurate, heights are measured for a random sample of 18 Begonias grown while being treated with the nutrient. The sample mean and sample standard deviation of those height measurements are 40 centimeters and 7 centimeters, respectively. **Assumptions and Objective:** Assume that the heights of treated Begonias are approximately normally distributed. Based on the sample, can it be concluded that the population mean height of treated Begonias, \( \mu \), is different from that reported in the journal? Use the 0.10 level of significance. **Steps for Analysis:** Perform a two-tailed test. Then complete the parts below: **Guidance for Computation:** Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) **Steps:** (a) **State the Hypotheses:** - Null Hypothesis (\( H_0 \)): \( \mu = 36 \) - Alternative Hypothesis (\( H_1 \)): \( \mu \neq 36 \) (b) **Determine the Type of Test Statistic:** - Use a Z-test for this analysis. (c) **Calculate the Test Statistic:** - Use the formula for the Z-test statistic. - Provide the calculated value. (d) **Find the p-value:** - Calculate the p-value corresponding to the observed test statistic. - Round to three or more decimal places. (e) **Conclusion:** - Determine whether the mean height of treated Begonias is different from that reported in the journal. - Indicate your conclusion with 'Yes' or 'No'. **Tools Provided:** A calculator with various statistical symbols and operators is provided for aid in computations. By following these steps, you can rigorously determine whether the treatment alters the mean height of Begonias compared to the reported value. Ensure all calculations are precise to make a valid statistical conclusion.
Transcribed Image Text:**Title: Two-Tailed Hypothesis Testing for Mean Height of Begonias** The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient is 36 centimeters. To check whether this is still accurate, heights are measured for a random sample of 18 Begonias grown while being treated with the nutrient. The sample mean and sample standard deviation of those height measurements are 40 centimeters and 7 centimeters, respectively. **Assumptions and Objective:** Assume that the heights of treated Begonias are approximately normally distributed. Based on the sample, can it be concluded that the population mean height of treated Begonias, \( \mu \), is different from that reported in the journal? Use the 0.10 level of significance. **Steps for Analysis:** Perform a two-tailed test. Then complete the parts below: **Guidance for Computation:** Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) **Steps:** (a) **State the Hypotheses:** - Null Hypothesis (\( H_0 \)): \( \mu = 36 \) - Alternative Hypothesis (\( H_1 \)): \( \mu \neq 36 \) (b) **Determine the Type of Test Statistic:** - Use a Z-test for this analysis. (c) **Calculate the Test Statistic:** - Use the formula for the Z-test statistic. - Provide the calculated value. (d) **Find the p-value:** - Calculate the p-value corresponding to the observed test statistic. - Round to three or more decimal places. (e) **Conclusion:** - Determine whether the mean height of treated Begonias is different from that reported in the journal. - Indicate your conclusion with 'Yes' or 'No'. **Tools Provided:** A calculator with various statistical symbols and operators is provided for aid in computations. By following these steps, you can rigorously determine whether the treatment alters the mean height of Begonias compared to the reported value. Ensure all calculations are precise to make a valid statistical conclusion.
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