9. An interval for the mean horn length (in inches) of...

9. An interval for the mean horn length (in inches) of African water buffalo that were raised on calcium supplements is $14.07 < \mu < 21.01$. Use this information to complete parts (a) through (c). (a) Use the interval to find the sample mean. $\bar{x} = $ ____ inches (Round to two decimal places as needed.) (b) What is the margin of error? $E = $ ____ inches (Round to two decimal places as needed.) (c) Write the interval in the form $\bar{x} \pm E$. $\bigcirc$ 17.54 $\pm$ 6.94 $\bigcirc$ 21.01 $\pm$ 3.47 $\bigcirc$ 17.54 $\pm$ 3.47 $\bigcirc$ 14.07 $\pm$ 3.47

Transcript

00:01 So we want to determine the margin of error for a 90 % confidence interval for mu, the population mean, and we're given that the sample standard deviation s is 35.

00:22 And we wanna find the margin of error for different sample sizes.

00:27 So before we do, let's kind of get the concept of what we're looking at.

00:30 So the confidence interval will be constructed with this formula, x bar plus minus t alpha over two, noting the degrees of freedom multiplied by s divided by the square of the sample size.

00:41 So we know s, right? it's 35.

00:45 And this, oh, by the way, this whole term is important.

00:48 This t times s over root n, this is our margin of error.

00:52 That's the margin of error right here.

00:56 We already know s.

00:58 The t we need to figure out.

00:59 This is gonna be 0 .10 because one minus the confidence level gives us our alpha.

01:05 So 0 .10.

01:06 The degrees of freedom is calculated as n minus one.

01:12 So this is gonna vary depending on our sample size, but we already know s, right? it's 35.

01:19 So we have n will determine the t value.

01:25 And let's go ahead and go through the first one.

01:31 So the first, i have a little table here.

01:34 The first one is sample size n is 15.

01:36 The degrees of freedom would be 14.

01:38 15 minus one is 14.

01:39 The t score is here.

01:41 And to get this, i use the following spreadsheet function, tinv.

01:49 And then you put in your alpha, 0 .10...

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