MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![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 7 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 3.4 hours with a standard deviation of 0.3 hours. For a random sample of 6 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 3.2 hours to paint each room with a standard deviation of 0.2 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 1 of 3:** State the null and alternative hypotheses for the test. Fill in the blank below,
\[
H_0 : \mu_1 = \mu_2
\]
\[
H_a : \mu_1\ ______\ \mu_2
\]](https://content.bartleby.com/qna-images/question/36a0cec1-64c3-4c43-b20d-bcd7032670a8/99053d1f-3973-41f5-8bc2-6120b12ec5a7/f5pwets_processed.jpeg)
Transcribed Image Text: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 7 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 3.4 hours with a standard deviation of 0.3 hours. For a random sample of 6 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 3.2 hours to paint each room with a standard deviation of 0.2 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 1 of 3:** State the null and alternative hypotheses for the test. Fill in the blank below,
\[
H_0 : \mu_1 = \mu_2
\]
\[
H_a : \mu_1\ ______\ \mu_2
\]
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