A marketing firm is doing research for an internet based...

A marketing firm is doing research for an Internet-based company. It wants to appeal to the age group of people who spend the most money online. The company wants to know if there is a difference in the mean amount of money people spend per month on Internet purchases depending on their age bracket. The marketing firm looked at two age groups, 18-24 years and 25-30 years, and collected the data shown in the following table. Let Population 1 be the amount of money spent per month on Internet purchases by people in the 18-24 age bracket and Population 2 be the amount of money spent per month on Internet purchases by people in the 25-30 age bracket. Assume that the population variances are not the same. Internet Spending per Month 18-24 Years 25-30 Years Mean Amount Spent 55.26 62.65 Standard Deviation 17.21 12.25 Sample Size 23 29 Step 1 of 2 : Construct an 80% confidence interval for the true difference between the mean amounts of money per month that people in these two age groups spend on Internet purchases. Round the endpoints of the interval to two decimal places, if necessary. Step 2 of 2: Interpret the confidence interval obtained in step 1.

Transcript

00:04 In this problem, you're asked to find a 80 % confidence interval for this scenario where they're looking at two age groups, the 18 and 24 -year -olds through 24 -year -olds and the 25 -year -olds, and they're trying to look at the amount of money spent on internet purchases for a month.

00:29 So there's some key numbers that you pick out of this.

00:33 And if you look at my table in black, i've written out just that this table is going to be the amount of money spent.

00:42 And that was on those internet purchases.

00:44 You've got a population one, which is your 18 to 24 year olds.

00:47 Your population 2 is 25 to 30 year olds.

00:49 And then i went through and i picked out.

00:52 It said the mean for the 18 to 24 olds was 55 .26, etc.

00:57 Etc.

00:59 It said the standard deviation was 17 .21 and that gave you the ends.

01:03 So in population one you had 23 in that sample.

01:06 So just recorded all in a table so that it's nice and neat to pull numbers.

01:11 And then when you go to do your confidence interval for this data, one of the things that you got to first focus on is which formula are you going to use? and so on my formula sheet, which i don't know if it'd be the same as the one that you are using.

01:28 I went and found the formula that you see here at the bottom of the screen, x bar 1 minus x bar 2, minus e, et cetera.

01:36 That's going to be the formula that you use to find a confidence interval for difference in means.

01:42 And that's the key wording that you see there in this problem is you want to find a confidence interval for the difference in means.

01:48 And so this would be your confidence interval.

01:51 And then in order to figure out how to get your e in this formula, then what you want to look at is, is your standard deviation known or unknown? if it is known, so your sigma is known, so your population standard deviation, if that's known, then you're going to use a formula for your e that has z in it.

02:17 But since in this case our sigma is unknown, because we know what s is, then we are going to want to use the formula that has the t sub c in it.

02:28 So if we're going to use the formula with t sub c in it, in order to get our t sub c, we're going to need to know our degrees of freedom.

02:43 And on the degrees of freedom for this formula, you want to pick your smallest of your two ends.

02:48 So in this case, it would be the 23.

02:52 And so for n equals 23, when you look at your degrees of freedom, degrees of freedom are n minus 1 and so if you do n minus 1 so 23 minus 1 you'll get 22 degrees of freedom and then you'll go to your chart that has your t -c values and unfortunately i am not able to show you my chart but pull out your chart and look for your chart that has your critical values for your students t distribution 22 degrees of freedom.

03:33 And then your level of confidence.

03:41 On this one, we are looking for an 80 % confidence interval.

03:46 And so you want to look at your level of confidence being 0 .8.

03:50 And so across the top, find your 0 .8 and go down to your 22 degrees of freedom.

03:57 And on my chart, i am getting 1 .321.

04:03 So hopefully that's the same chart that you use for your class.

04:05 Class, 1 .321.

04:28 Then you're going to multiply that by plugging your number, so your s1 is 17 .21, and you need to square just that number over your n1, so n1 is 23, and then add to that your s2, which is 12 .25, and square that and divide that by your n2, which is 29.

05:14 And i am getting an e of 5 .6 .13 for that.

05:21 And so it takes a little bit of doing to get a calculator, but you should be able to do that part...

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