The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient is 33 centimeters. To check whether this is still accurate, heights are measured for a random sample of 21 Begonias grown while being treated with the nutrient. The sample mean and sample standard deviation of those height measurements are 32 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. **Knowledge Check: Hypothesis Testing****Question 3**(a) **State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \)**.\[ H_0: \boxed{\ } \]\[ H_1: \boxed{\ } \](b) **Determine the type of test statistic to use.**\[ \boxed{\left(\text{Choose one}\right)} \] \(\ because \ \) (c) **Find the value of the test statistic. (Round to three or more decimal places.)**\[ \boxed{\ } \](d) **Find the two critical values. (Round to three or more decimal places.)**\[ \boxed{\ } \ \text{and} \ \boxed{\ } \](e) **Can it be concluded that the mean height of treated Begonias is different from that reported in the journal?**\[ \boxed{\text{Yes}} \ \text{ } \boxed{\text{No}} \]**Options for Input Fields and Equations**- On the right side of the figure, a series of mathematical symbols are provided in a clickable panel for input convenience. The symbols include various types of statistical notations, including but not limited to: \[ \mu, \sigma, p, \pm, X^2, t, <, >, \leq, \geq, = \]- Symbols and equations needed for hypothesis testing can be entered using this panel.**Final Submission Options**- **I Don't Know** - **Submit****Miscellaneous**- The page footer contains some basic browsing options and application icons.- This exercise is part of ALEKS, a McGraw Hill platform for educational assignments and assessments.- The thermometer icon indicates a current temperature of 76°F and sunny weather.- The timestamp at the bottom right indicates that this activity was accessed on 06/07/2022 at 10:44 AM.Use this structured layout to perform your hypothesis testing efficiently and accurately based on the given problem.

The provided information is x¯=32s=7n=21α=0.05The degrees od freedom is df=n-1=21-1=20

Answered: (a) State the null hypothesis Ho and…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient is 33 centimeters. To check whether this is still accurate, heights are measured for a random sample of 21 Begonias grown while being treated with the nutrient. The sample mean and sample standard deviation of those height measurements are 32 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.

**Knowledge Check: Hypothesis Testing**

**Question 3**

(a) **State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \)**.

\[ H_0: \boxed{\ } \]

\[ H_1: \boxed{\ } \]

(b) **Determine the type of test statistic to use.**

\[ \boxed{\left(\text{Choose one}\right)} \] \(\ because \ \)

(c) **Find the value of the test statistic. (Round to three or more decimal places.)**

\[ \boxed{\ } \]

(d) **Find the two critical values. (Round to three or more decimal places.)**

\[ \boxed{\ } \ \text{and} \ \boxed{\ } \]

(e) **Can it be concluded that the mean height of treated Begonias is different from that reported in the journal?**

\[ \boxed{\text{Yes}} \ \text{ } \boxed{\text{No}} \]

**Options for Input Fields and Equations**

- On the right side of the figure, a series of mathematical symbols are provided in a clickable panel for input convenience. The symbols include various types of statistical notations, including but not limited to:
\[ \mu, \sigma, p, \pm, X^2, t, <, >, \leq, \geq, = \]

- Symbols and equations needed for hypothesis testing can be entered using this panel.

**Final Submission Options**

- **I Don't Know**
- **Submit**

**Miscellaneous**

- The page footer contains some basic browsing options and application icons.
- This exercise is part of ALEKS, a McGraw Hill platform for educational assignments and assessments.
- The thermometer icon indicates a current temperature of 76°F and sunny weather.
- The timestamp at the bottom right indicates that this activity was accessed on 06/07/2022 at 10:44 AM.

Use this structured layout to perform your hypothesis testing efficiently and accurately based on the given problem.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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