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 37 centimeters and 7 centimeters, respectively. 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 0.05 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 H, and the alternative hypothesis H₁. H₂:0 H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places,) 0 (e) Can it be concluded that the mean height of treated Begonias is different from that reported in the journal? OYes No H X 0-0 O X O S 00 OSO <口 Р ô 020 >O Espe ? 18 B As V
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 37 centimeters and 7 centimeters, respectively. 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 0.05 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 H, and the alternative hypothesis H₁. H₂:0 H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places,) 0 (e) Can it be concluded that the mean height of treated Begonias is different from that reported in the journal? OYes No H X 0-0 O X O S 00 OSO <口 Р ô 020 >O Espe ? 18 B As V
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Solution:**
(a) The null and alternative hypotheses are:
\( H_0: \mu = 36 \) vs \( H_1: \mu \neq 36 \)
(b) The type of the test statistic is 't' because the population standard deviation is unknown.
(c) The test statistic is
\[
t = \frac{\overline{X} - \mu}{s/\sqrt{n}} = \frac{37 - 36}{7/\sqrt{18}}
\]
\( t = 0.606 \) (3 decimal places)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a1b2b9d-136a-4887-96f9-8b3f93dfa3b9%2F840288e7-ef79-4042-b92d-c9563bf01039%2Fzu35z3zk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solution:**
(a) The null and alternative hypotheses are:
\( H_0: \mu = 36 \) vs \( H_1: \mu \neq 36 \)
(b) The type of the test statistic is 't' because the population standard deviation is unknown.
(c) The test statistic is
\[
t = \frac{\overline{X} - \mu}{s/\sqrt{n}} = \frac{37 - 36}{7/\sqrt{18}}
\]
\( t = 0.606 \) (3 decimal places)
.)
**(a)** State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).
\[ H_0: \]
\[ H_1: \]
**(b)** Determine the type of test statistic to use.
(Choose one) ⬇️
**(c)** Find the value of the test statistic. (Round to three or more decimal places.)
\[\_\_\_\_\_\_\_\_\_\_ \]
**(d)** Find the \( p \)-value. (Round to three or more decimal places.)
\[\_\_\_\_\_\_\_\_\_\_ \]
**(e)** Can it be concluded that the mean height of treated Begonias is different from that reported in the journal?
- [ ] Yes
- [ ] No
### Additional Notes
- The interface includes a selection of symbols typically used in statistical formulas, such as \( \mu, \overline{x}, s, \hat{p} \).
- Use statistical software or a calculator to compute the test statistic and the p-value based on the sample data provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a1b2b9d-136a-4887-96f9-8b3f93dfa3b9%2F840288e7-ef79-4042-b92d-c9563bf01039%2Fc9koz4n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Confidence Intervals and Hypothesis Testing
### Hypothesis Test for the Population Mean: T Test Using the P Value
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 37 centimeters and 7 centimeters, respectively.
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 0.05 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 \( H_0 \) and the alternative hypothesis \( H_1 \).
\[ H_0: \]
\[ H_1: \]
**(b)** Determine the type of test statistic to use.
(Choose one) ⬇️
**(c)** Find the value of the test statistic. (Round to three or more decimal places.)
\[\_\_\_\_\_\_\_\_\_\_ \]
**(d)** Find the \( p \)-value. (Round to three or more decimal places.)
\[\_\_\_\_\_\_\_\_\_\_ \]
**(e)** Can it be concluded that the mean height of treated Begonias is different from that reported in the journal?
- [ ] Yes
- [ ] No
### Additional Notes
- The interface includes a selection of symbols typically used in statistical formulas, such as \( \mu, \overline{x}, s, \hat{p} \).
- Use statistical software or a calculator to compute the test statistic and the p-value based on the sample data provided.
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