00:01
So we're giving an interesting question.
00:02
Last year, 20 % of all teenagers purchased a new iphone.
00:05
This year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new phone.
00:12
To test whether the percentage has decreased, the test statistic is.
00:17
So let's briefly run through what a hypothesis test is to get to your test statistic.
00:25
So we are first looking at a null hypothesis is saying that our, population parameter has stayed the same.
00:34
It's going to be 20 % with our alternate hypothesis saying that somehow our true percentage of teens that buy iphones is less than 0 .2 because we're looking for things that would be less than those.
00:54
So before you jump into this, it's always good to check your assumptions and conditions.
01:05
Namely, the sample was selected.
01:08
This was a simple random sample.
01:10
It was said that they're selected randomly.
01:13
So this gives you that they are independent.
01:20
You also have to check n p hat and n q hat are both greater than or equal to 10.
01:31
Now, p hat is your sample statistic that you're given.
01:35
So 39 out of 260, which is 0 .15.
01:39
So just briefly, 260 times 0 .15, that's going to be greater than or equal to 10.
01:45
And likewise, 260 times 0 .85 is also greater than or equal to 10.
01:51
So our sample is large enough to use a normal model.
02:05
Now, this is important because this is where most of this data comes from.
02:09
So our normal model is going to be centered at our true population proportion.
02:16
0 .2 and it's going to have our standard error of our parameter.
02:25
So just so you know, standard error is equal to the square root of pq, so 0 .2 times 0 .8 over 2 .2 .2.
02:39
260, which is our sample size.
02:43
So i will do that math really quickly on a calculator.
02:46
We want the square root of 0 .2 times 0 .8 over 260.
02:59
So this gives us a standard error of 0 .024807.
03:05
So let's write that right there...