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This is problem 80 out of section 9 .3.
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This problem here deals with filling cola bottles.
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A company wants to fill their cola bottles to 300 milliliters.
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But every so often, they take a random sample, and this time they took a random sample of six bottles and found out how much was in each bottle, and you have those six values listed there.
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And they want to know, do these data provide convincing evidence that the mean amount of cola in all the bottles filled that day, differes.
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So differs.
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That's a keyword here.
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So our statement, again, the state plan do conclude.
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Our statement here, we're going to perform a one sample.
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We're in a mean here, so it's going to be a t, and we're doing a test here.
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We're not doing a confidence interval.
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And we're going to do this at an alpha value of 0 .05.
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Our null hypothesis, always when we're doing a test, null hypothesis, the company wants mu to be 300.
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The alternate, this is where that word differ comes in, because remember we can have three things here for the alternate, less than, greater than, or not equals to.
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Because they want it differs, they don't care whether it's bigger or smaller.
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They just want to know if it differs, so we go not equal to 300.
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Our plan then, our plan, we need to check three things, random.
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And it says the six, bottles are randomly selected.
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10 % rule.
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I hope six bottles is less than 10 % of all the bottles produced.
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If not, that means they're filling less than 60 bottles.
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And then finally, large counts.
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Well, large counts, n equals six.
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Oh boy, and we want to compare that to 30.
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We cannot do the clt here, which means we need to look at graphs.
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We always want that sample size to be 30 or larger.
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In this case, it's not.
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So we will need to plug those six numbers into list one into your calculator, and then graph them.
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I like to do the box plot, which this box plot looks really pretty good.
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And i like to do the histogram.
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And the histogram also looks good.
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Remember what we're looking for.
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In this one, we're looking for outliers.
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There do not appear there be any outliers, so we're good.
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In the histogram, we're looking for skew.
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There does not appear to be skew.
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So we are good...