Question
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
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 the data from a random sample of 6 medium-size rooms. He determined that the mean amount of time that it took him to paint each room was 4.2 hours with a standard deviation of 0.5 hours. For a random sample of 4 medium sized rooms that he painted using the new tool he found that it took him a mean of 3.9 hours to paint each room with a standard deviation of 0.7 hours. At the 0.10 level, can Gary conclude that his mean time when using painting a medium size room without the tool was greater than his mean time when using the tool? Assume the population variances are equal.
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