Answered: O H: At least two of the population…

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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### Hypothesis Testing Example

**Hypotheses:**

- $ H_0 $: At least two of the population means are equal.
- $ H_a $: At least two of the population means are different.

**Options:**

1. $ H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4 $

$ H_a: $ Not all the population means are equal.

2. $ H_0: \mu_1 + \mu_2 \neq \mu_3 + \mu_4 $

$ H_a: \mu_1 = \mu_2 = \mu_3 = \mu_4 $

3. $ H_0: $ Not all the population means are equal.

$ H_a: \mu_1 = \mu_2 = \mu_3 = \mu_4 $

4. $ H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4 $

$ H_a: \mu_1 \neq \mu_2 \neq \mu_3 \neq \mu_4 $

**Steps:**

1. **Find the value of the test statistic.**
- (Round your answer to two decimal places.)
- Test statistic = [Input box]

2. **Find the p-value.**
- (Round your answer to four decimal places.)
- $ p\text{-value} = $ [Input box]

**Conclusion:**

Choose one:
- ☐ Do not reject $ H_0 $. There is not sufficient evidence to conclude that the mean drying times for the four robots are not all equal.
- ☐ Do not reject $ H_0 $. There is sufficient evidence to conclude that the mean drying times for the four robots are not all equal.
- ☐ Reject $ H_0 $. There is not sufficient evidence to conclude that the mean drying times for the four robots are not all equal.
- ☐ Reject $ H_0 $. There is sufficient evidence to conclude that the mean drying times for the four robots are not all equal.

$Certainly! Here is a transcription and explanation suitable for an educational website: --- Title: Analyzing Paint-Drying Times of Robots **Introduction:** Understanding how long it takes paint to dry can significantly impact the production efficiency of a business, especially in auto body and paint sectors. A critical question to consider is: "Do all paint-drying robots have the same drying time?" By examining the drying times of different robots, businesses can optimize their processes. **Experimental Setup:** To explore this question, five drying times for each brand of paint-drying robots were sampled. The drying time in minutes until the paint was sufficiently dry for a second coat was noted. Below is the data recorded for four different types of robots. **Data Table:** | | Robot 1 | Robot 2 | Robot 3 | Robot 4 | |--------|---------|---------|---------|---------| | **1st Sample** | 137 | 145 | 138 | 127 | | **2nd Sample** | 126 | 135 | 136 | 144 | | **3rd Sample** | 137 | 145 | 133 | 132 | | **4th Sample** | 149 | 139 | 134 | 134 | | **5th Sample** | 124 | 137 | 141 | 151 | **Statistical Testing:** At a significance level ($\alpha$) of 0.05, a test is conducted to examine if there are differences in mean drying times across the robots. **Hypotheses:** 1. **Null Hypothesis ($H_0$)**: All population means are equal. This implies that there is no significant difference in the drying times of the robots. 2. **Alternative Hypothesis ($H_a$)**: At least two of the population means are different, suggesting that not all robots have the same drying time. Options for hypotheses formulation are as follows: - $H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4$ - $H_a: \text{At least two of the population means are different}$ **Conclusion:** The analysis performed based on this setup will help determine if the difference in drying times is statistically significant. This information is crucial$

Transcribed Image Text:Certainly! Here is a transcription and explanation suitable for an educational website: --- Title: Analyzing Paint-Drying Times of Robots **Introduction:** Understanding how long it takes paint to dry can significantly impact the production efficiency of a business, especially in auto body and paint sectors. A critical question to consider is: "Do all paint-drying robots have the same drying time?" By examining the drying times of different robots, businesses can optimize their processes. **Experimental Setup:** To explore this question, five drying times for each brand of paint-drying robots were sampled. The drying time in minutes until the paint was sufficiently dry for a second coat was noted. Below is the data recorded for four different types of robots. **Data Table:** | | Robot 1 | Robot 2 | Robot 3 | Robot 4 | |--------|---------|---------|---------|---------| | **1st Sample** | 137 | 145 | 138 | 127 | | **2nd Sample** | 126 | 135 | 136 | 144 | | **3rd Sample** | 137 | 145 | 133 | 132 | | **4th Sample** | 149 | 139 | 134 | 134 | | **5th Sample** | 124 | 137 | 141 | 151 | **Statistical Testing:** At a significance level ($\alpha$) of 0.05, a test is conducted to examine if there are differences in mean drying times across the robots. **Hypotheses:** 1. **Null Hypothesis ($H_0$)**: All population means are equal. This implies that there is no significant difference in the drying times of the robots. 2. **Alternative Hypothesis ($H_a$)**: At least two of the population means are different, suggesting that not all robots have the same drying time. Options for hypotheses formulation are as follows: - $H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4$ - $H_a: \text{At least two of the population means are different}$ **Conclusion:** The analysis performed based on this setup will help determine if the difference in drying times is statistically significant. This information is crucial

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