In this video I'm going to show you how to use the work sheet that I provided for

you to do one TL test, for the difference between two sample proportions,

as well as when the hypothesize more than as your difference between the two.

I'm going to use the example use that’s the fast food chain that is testing in

revise work flow, and they're testing the new design versus the current design, and

they want a better than 20% improvement in terms of proportion of customers who

can get their orders completed within 4 minutes.

So they have 7,600 out of 10,000 customers who

get their orders within four minutes in the current design.

And for the new design, 5,400 out of 6,000 that get their order within four minutes.

And we're going to test this to see if there is a 5% level of significance,

we can show that there is a 20% improvement in that proportion.

So our now hypothesis would be that, really there is not that

much of a difference between the two so P1-P2 is less than equal to 20%.

Here P1 is going to represent the current design proportion of

customers who get their orders within 4 minutes under current design.

And P2 is going to show proportion of customers who get their

orders within 4 minutes under new design.

So clearly the, so that alternate would be the compliment.

So now let's go and now check how we would do this in our worksheet.

So key one count of events, how many customers, 7,600 out of 10,000 got

their orders within four minutes, and for the new design 5,400 out of 6,000.

Our level of significance is 0.05, and the hypothesized difference is 20%.

Now that you have entered this, these values start showing up, so

let me scroll down to our output.

Now we're doing the one-tail test and you would see,

that I have two areas for one-tail test, right here.

So you need to focus on the part that applies to your particular problems.

So I want you to look at your null hypothesis and

decide whether you have to use the first one or the second one that you see.

So going back a null hypothesis Is less than or equal to a value.

So I didn't make this as sophisticated.

Everything shows as less than or equal to 0.

What I want you to pay attention to is just whether p1 minus p2 is less than or

equal to something or greater than something.

So in our case we are only going to focus on this part because this is the part that

matches what we want to see p1- p2 less than or equal to some value.

And now if you look at your p value, you would see that it's a large number and

it's greater than 0.05, so you do not reject the null hypothesis.

We will not reject this which means we have not shown that it would do

better than 20%.

Now would be when you want to know what is the confidence interval for

the difference between the two designs.

We said that it was at least 20%, but what is it, what is the difference?

Is it 19%, would it be different if it was 19%?

Would management revise this idea, so

it might be a good idea to provide that confidence interval as well.

So here most everything that you need is calculated for

you based on the formula that you need the differences between the two samples, and

that you can see here is 14%, and you need to find that margin of error.

And I have given you the standard error and

what you need to do is find out which z value you will use.

Now let me give you an idea about the z value again.

We did a one tailed test and in a One-Tail test the entire 5% is one side.

So we did we the left side.

So 5% was right here and the other 5% for margin of error we need

a positive as well as a negative, that margin of error gets added, plus or minus.

So confidence interval is always a Two-Tail test.

So if I use a 5% for One-Tail, you would see that it's 1.6 645,

so this is 1.645 on to the right and then -1.645 into the left.

So if I use that value, what is the resulting confidence interval

is going to be a 90% confidence interval, because there is a 5 Percent chance

of getting it wrong in both tails of our distribution.

So if I use 1.645, I will get the 90% confidence interval.

If you want the 95% confidence interval, you should use 1.96.

So this is saying that it's already splitting the 5% into two-tails, and

that's what I want for my confidence interval if

I want a 95% confidence interval, actually be using this value.

So now that we have this, we can say margin of error is simply

the 1.96 times the standard error,

and now I can find my lower bound and the upper bound.