Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to understand the assumptions underlying one-way ANOVA hypothesis testing. Here's our problem statement: The company data table contains chest deceleration measurements in g (where g is the force of gravity) from samples of small, midsize, and large cars. Shown are the technology results for analysis of variance of this data table. Assume that a researcher plans to use a 5% significance level to test the claim that the different size categories have the same mean chest deceleration in the standard crash test. Complete Parts A and B below.
OK, Part A says, "What characteristic of the data specifically indicates that one-way analysis of variance should be used?" Well, let's go ahead and take a look at our data. I click on this icon here; it shows us our data. Here's our population of data, or rather the sampling that they took. And we see that there's three sizes here --- small, midsize, and large. So everything's being categorized according to the one category, which we would say is size. But there's three different options to choose from. And that's really the key characteristic here, that you've got different categories of the same type that you're trying to compare. Of course there's more than two of them. So that combination calls for one-way ANOVA testing.
So what are our options here? "The measurements are characterized according to the one characteristic of size." Yep. That's pretty much it. But let's check the other options just to make sure. "There are three samples of measurements." Well, yeah, three lends to one-way ANOVA testing, but just having three samples alone is not enough. The key characteristic is categorization according to one characteristic. "The population means are approximately normal." Well, we hope they are, but they may not be. "Nothing specifically indicates that one-way analysis of variance should be used." Yeah, that's not true. So we're going to go with Answer option A here. Good job!
Now Part B says, "If the objective is to test the claim that the three size categories have the same mean chest deceleration, why is the method referred to as analysis of variance?" Well, it's because we're analyzing a variance. And the variance that we're analyzing is a common population variance. So we're estimating the population variance, usually from two different directions. And that's what the method is actually based on.
So let's see what our answer options say here. Yeah, right here. "Estimates of common population variance." Boom. That's what we're looking for. Excellent!
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