Please only answer PART B **Three Calculus Classes Take the Same Test and the Scores Are Recorded**### Oneway Analysis of Score by ClassThe analysis is displayed in a box plot graph, illustrating the test scores for three different calculus classes, labeled A, B, and C. - **Box Plot Explanation:** - **Y-Axis:** Represents score values ranging from 0 to 100. - **X-Axis:** Represents each class (A, B, and C). - Each box represents the interquartile range (IQR) where the middle 50% of scores lie. - The horizontal line inside each box represents the median score. - The "whiskers" extend to the smallest and largest values within 1.5 IQR from the lower and upper quartile. - Dots outside the whiskers indicate outliers.### Statistical Analysis Summary#### Summary of Fit- **Rsquare:** 0.000288- **Adj Rsquare:** -0.04732- **Root Mean Square Error:** 12.09697- **Mean of Response:** 77.08889- **Observations (or Sum Wgts):** 45#### Analysis of Variance (ANOVA)- **Source:** Differentiates between the variance within groups and between groups.- **DF (Degrees of Freedom):** - Total: 44 - Between Groups (Class): 2 - Within Groups (Error): 42- **Sum of Squares:** - Class: 1.9111 - Error: 6877.7333 - Total: 6879.6444- **Mean Square:** - Class: 0.9556 - Error: 158.994- **F Ratio:** 0.0060- **Prob > F:** 0.9940 (indicating no significant difference)#### Means for Oneway ANOVA- **Level:** Class A, B, C - **Number:** 15 each - **Mean Scores:** - A: 76.8000 - B: 77.2000 - C: 77.2867 - **Std Error:** 3.2657 - **Confidence Intervals (95%):** - **Lower 95% ### (a)The math department is interested in seeing if the three different teachers have an effect on the students' scores, so they want to test if the mean scores in all three classes are the same or not. What is the hypothesis test to be done?- ○ $ H_0: $ means are not all equal $ H_1: \mu_1 = \mu_2 = \mu_3 $- ○ $ H_0: \mu_1 > \mu_2 = \mu_3 $ $ H_1: \mu_1 \leq \mu_2 = \mu_3 $- ○ $ H_0: \mu_1 = \mu_2 = \mu_3 $ $ H_1: \mu_1 \neq \mu_2 \neq \mu_3 $- ○ $ H_0: \mu_1 = \mu_2 = \mu_3 $ $ H_1: \mu_1 = \mu_2 \neq \mu_3 $- ○ $ H_0: \mu_1 > \mu_2 > \mu_3 $ $ H_1: \mu_2 > \mu_3 $- ○ $ H_0: \mu_1 = \mu_2 = \mu_3 $ $ H_1: $ means are not all equal### (b)The test is done with a 95% confidence level. Find the test statistic, and p-value. (Round your test statistic and p-value to three decimal places).- Test statistic: [ ]- p-value: [ ]### (c)The department has decided to give a raise to a teacher if his/her class scored significantly higher. Using the hypothesis test, find the correct conclusion.- The null hypothesis should [Select]. - The means from the three classes [Select] statistically different. - The department [Select] award a raise to a teacher.You may need to use the appropriate table in the Appendix of Tables to answer this question.

The test statistic and the p-value can be obtained from the given output.

Answered: The test is done with a 95% confidence…

The test is done with a 95% confidence level. Find the test statistic, and p-value. (Round your test statistic and p-value to three decimal places). test statistic p-value

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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Question

Please only answer PART B

**Three Calculus Classes Take the Same Test and the Scores Are Recorded**

### Oneway Analysis of Score by Class

The analysis is displayed in a box plot graph, illustrating the test scores for three different calculus classes, labeled A, B, and C.

- **Box Plot Explanation:**
- **Y-Axis:** Represents score values ranging from 0 to 100.
- **X-Axis:** Represents each class (A, B, and C).
- Each box represents the interquartile range (IQR) where the middle 50% of scores lie.
- The horizontal line inside each box represents the median score.
- The "whiskers" extend to the smallest and largest values within 1.5 IQR from the lower and upper quartile.
- Dots outside the whiskers indicate outliers.

### Statistical Analysis Summary

#### Summary of Fit

- **Rsquare:** 0.000288
- **Adj Rsquare:** -0.04732
- **Root Mean Square Error:** 12.09697
- **Mean of Response:** 77.08889
- **Observations (or Sum Wgts):** 45

#### Analysis of Variance (ANOVA)

- **Source:** Differentiates between the variance within groups and between groups.
- **DF (Degrees of Freedom):**
- Total: 44
- Between Groups (Class): 2
- Within Groups (Error): 42
- **Sum of Squares:**
- Class: 1.9111
- Error: 6877.7333
- Total: 6879.6444
- **Mean Square:**
- Class: 0.9556
- Error: 158.994
- **F Ratio:** 0.0060
- **Prob > F:** 0.9940 (indicating no significant difference)

#### Means for Oneway ANOVA

- **Level:** Class A, B, C
- **Number:** 15 each
- **Mean Scores:**
- A: 76.8000
- B: 77.2000
- C: 77.2867
- **Std Error:** 3.2657
- **Confidence Intervals (95%):**
- **Lower 95%

### (a)

The math department is interested in seeing if the three different teachers have an effect on the students' scores, so they want to test if the mean scores in all three classes are the same or not. What is the hypothesis test to be done?

- ○ $ H_0: $ means are not all equal
$ H_1: \mu_1 = \mu_2 = \mu_3 $

- ○ $ H_0: \mu_1 > \mu_2 = \mu_3 $
$ H_1: \mu_1 \leq \mu_2 = \mu_3 $

- ○ $ H_0: \mu_1 = \mu_2 = \mu_3 $
$ H_1: \mu_1 \neq \mu_2 \neq \mu_3 $

- ○ $ H_0: \mu_1 = \mu_2 = \mu_3 $
$ H_1: \mu_1 = \mu_2 \neq \mu_3 $

- ○ $ H_0: \mu_1 > \mu_2 > \mu_3 $
$ H_1: \mu_2 > \mu_3 $

- ○ $ H_0: \mu_1 = \mu_2 = \mu_3 $
$ H_1: $ means are not all equal

### (b)

The test is done with a 95% confidence level. Find the test statistic, and p-value. (Round your test statistic and p-value to three decimal places).

- Test statistic: [ ]
- p-value: [ ]

### (c)

The department has decided to give a raise to a teacher if his/her class scored significantly higher. Using the hypothesis test, find the correct conclusion.

- The null hypothesis should [Select].
- The means from the three classes [Select] statistically different.
- The department [Select] award a raise to a teacher.

You may need to use the appropriate table in the Appendix of Tables to answer this question.

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