Gary has discovered a new painting tool to help him in his work. If he can prove to himself that the painting tool reduces the amount of time it takes to paint a room, he has decided to invest in a tool for each of his helpers as well. From records of recent painting jobs that he completed before he got the new tool, Gary collected data for a random sample of 6 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 3.8 hours with a standard deviation of 0.2 hours. For a random sample of 8 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 3.4 hours to paint each room with a standard deviation of 0.3 hours. At the 0.05 level, can Gary conclude that his mean time for painting a medium-sized room without using the tool was greater than his mean time when using the tool? Assume that both populations are approximately normal and that the population variances are equal. Let painting times without using the tool be Population 1 and let painting times when using the tool be Population 2. Step 3 of 3: Draw a conclusion and interpret the decision. 田 Tables E Keypad Answer Keyboard Shortcuts We reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance to support Gary's claim that his mean time for painting a medium-sized room without using the tool is greater than his mean time when using the tool. We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance to support Gary's claim that his mean time for painting a medium-sized room without using the tool is greater than his mean time when using the tool. We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance to support Gary's claim that his mean time for painting a medium-sized room without using the tool is greater than his mean time when using the tool. We reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance to support Gary's claim that his mean time for painting a medium-sized room without using the tool is greater than his mean time when using the tool.
Gary has discovered a new painting tool to help him in his work. If he can prove to himself that the painting tool reduces the amount of time it takes to paint a room, he has decided to invest in a tool for each of his helpers as well. From records of recent painting jobs that he completed before he got the new tool, Gary collected data for a random sample of 6 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 3.8 hours with a standard deviation of 0.2 hours. For a random sample of 8 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 3.4 hours to paint each room with a standard deviation of 0.3 hours. At the 0.05 level, can Gary conclude that his mean time for painting a medium-sized room without using the tool was greater than his mean time when using the tool? Assume that both populations are approximately normal and that the population variances are equal. Let painting times without using the tool be Population 1 and let painting times when using the tool be Population 2. Step 3 of 3: Draw a conclusion and interpret the decision. 田 Tables E Keypad Answer Keyboard Shortcuts We reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance to support Gary's claim that his mean time for painting a medium-sized room without using the tool is greater than his mean time when using the tool. We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance to support Gary's claim that his mean time for painting a medium-sized room without using the tool is greater than his mean time when using the tool. We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance to support Gary's claim that his mean time for painting a medium-sized room without using the tool is greater than his mean time when using the tool. We reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance to support Gary's claim that his mean time for painting a medium-sized room without using the tool is greater than his mean time when using the tool.
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
Transcribed Image Text:**Transcription and Explanation for Educational Use**
**Scenario Overview:**
Gary has discovered a new painting tool to help him in his work. He wants to determine if the tool reduces the time it takes to paint a room. Records from previous painting jobs before acquiring the tool show that it took him an average of 3.8 hours to paint each medium-sized room, with a standard deviation of 0.2 hours based on a random sample of 6 rooms. Using the new tool, Gary found that it took him an average of 3.4 hours, with a standard deviation of 0.3 hours, to paint a random sample of 8 medium-sized rooms. He wants to know if the mean painting time without the tool is greater than the mean painting time with the tool at a significance level of 0.05.
**Step 3 of 3: Decision and Interpretation**
Given the information above, the task is to draw a conclusion from a hypothesis test.
**Options for Conclusion:**
1. **Option 1:**
"We reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance to support Gary’s claim that his mean time for painting a medium-sized room without using the tool is greater than his mean time when using the tool."
2. **Option 2:**
"We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance to support Gary’s claim that his mean time for painting a medium-sized room without using the tool is greater than his mean time when using the tool."
3. **Option 3:**
"We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance to support Gary’s claim that his mean time for painting a medium-sized room without using the tool is greater than his mean time when using the tool."
4. **Option 4:**
"We reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance to support Gary’s claim that his mean time for painting a medium-sized room without using the tool is greater than his mean time when using the tool."
**Explanation:**
- **Rejecting the Null Hypothesis:** Suggests there is enough statistical evidence to support a claim.
- **Failing to Reject the Null Hypothesis:** Indicates there is not enough statistical evidence to support a claim.
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