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In this video, we're going to look at how we find a point estimate and construct confidence intervals for the population mean if we are given a set of data.
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Now, with this, we are going to utilize the graphing calculator to see how to do that.
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What i've done so far is i've gone to stat and under the stat menu in the edit, i've entered the data that was given, 12 .25, 13 .49, etc.
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So that i entered into l1 in my calculator.
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Now, a point estimate for the population mean mu is your sample mean x bar.
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So once that data is entered into the calculator, you push stat and calculate 1 var stat and enter.
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And my data is in l1 and i don't have anything in my frequency list.
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So i'll go ahead and i'll calculate that.
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And the top line is going to report that my point estimate from you is my sample mean x bar equal to 15 .382.
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So that's part a.
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Next, it asks us to look at a box pot and a normal.
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Probability plot to see if we can utilize the methods from this section.
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Well, when you look at the pictures of that, all the data lie in the bounds of the probability plot.
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And from the box plot, using the information about the lower fronts and the upper fronts and checking to see, we notice that there are no outliers.
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So because we have that particular information, we can go along with the process.
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Now next, we want to construct a 95 % confidence interval to estimate the population mean price.
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And since this was in money for price, we can even go back up here and say that our point estimate is $15 .38.
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Now, coming down and constructing this 95 % confidence interval to estimate the mean, the population mean price, we can utilize the tables in our scientific calculator by running the information through x bar minus t sub alpha over two times s divided by the square root of n for your lower bound and x bar plus t sub alpha.
03:23
Of alpha over 2 times s over the square of n for my upper bound.
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Now here, the sample mean was our 15 .382.
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Our sample standard deviation we also get for the readout on the calculator.
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That's the s subax, 2 .343.
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Our sample size n, well, the data, i had 10 pieces of data, and that's also reported on this screen as well, and is equal to 10.
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If you didn't have the advantage of using your graphing calculator, you would just count the number of data values that were given to you, and that is 10.
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And then for our t -sab alpha over 2, we would look at first finding alpha, and alpha.
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Is found by one minus the confidence level in decimal form.
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So changing that to decimal, that would be 0 .95.
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1 minus 0 .95 is 0 .05 .05.
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Taking that and dividing it by 2, that's 0 .025.
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And then our degrees of freedom is n minus 1.
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N is 10, so n minus 1 is 9.
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Looking under the column heading of 0 .025 for the right tail information on the table.
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And across from your degrees of freedom of nine, you'll get your critical value.
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Or if you're allowed to use a graphing calculator, you would go second distribution, come down to inverse t, push enter.
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And here i need to enter the area left of the critical value...