The direct mail marketing firm has started using an App to distribute coupons.

Out of 1000 randomly selected customers that were using the App,

94 bought the product.

They're wondering if this rate is different from

their 7 percent success rate and you want

to test this at 5 percent level of significance.

So we're going to do hypothesis testing again here.

The difference here is that we are not assuming

that the app is more successful or less successful.

We just want to see if it's any different.

So to rewrite this problem as a set of hypothesis,

we would say that the null hypothesis is that

the proportion of people who will buy will not

be any different than what we have had before,

which is 7 percent.

And the alternate is that this new way of marketing might be different.

So it's the test of equality versus inequality,

which means that it's a two tail test.

Everything else will remain the same,

except how the alpha is split up.

The alpha in this case is going to be split up in both sides of the tail.

So we are different,

if we have more people buying or less people

buying and that 5 percent that you're talking about is going to be right here.

So when we calculate our 'P' value and we

compare it to Alpha we have

one of two options and I will talk about that when I get to it.

So one of the things that I want to do is that first

of all find what was a sample proportion here.

And the sample proportion here is that 94 out of 1000 purchased this product,

so then 9.4 percent of the customers who received this coupon on the app

bought the product and they want to know that if point 0.094 is different that 7 percent.

The sample size that they were looking at was

1000 customers that they had tested this on.

And level of significance here it is point 0.05.

So now we can calculate 'Z' and 'Z' will be calculated by taking 'P' hat minus

'P' zero divided by the square root of 'P' zero times one minus 'P' zero divided by 'n'.

And I'm going to just calculate that right here.

So it's equal to parentheses, 'P' hat,

that is our 'P' hat minus 'P' zero

which is right here divided by square root by of 'P' zero.

Remember, this is 'P' zero 0.07 times one minus 'P' zero.

And the whole thing divided by sample size of 1000 and

close the parentheses and the 'Z' value we get is 2.97,

so the hypothesized proportion was seven percent,

but we got a sample that is 9.47

percent and that is to the right of the mean and it will be somewhere here.

So in order for me to know what is

the 'P' value remember the 'P' value if I put "NORM.S.DIST"

its going to return everything to the left of it.

So in order for me to get what is in the tail,

I need to do a one minus.

So I'm going to say it's equal to one minus NORM.S.DIST

and then take the 'Z' value and one.

This is going to return point 0.001.

Now, this is what is in the right tail but remember

because we're doing a two tail test you have two options here.

One is you take this value,

this 'P'value because it's a two tail test,

0.001 would be on the right tail point,

0.001 would be on the left tail.

These are the probability of finding samples that are more than

2.97 Standard errors away from the mean of the sampling distribution.

So, they can be either on the rightt side or

the left side because they will reject the null hypothesis on either end.

So you have two options.

One is to take point 0.00147 and multiply it by two and

then compare to half of 0.05 or you can just compare the 'P' value that you see here,

with the half of alpha.

Either one doesn't make a difference.

So to be consistent with my my teaching in the PowerPoint.

I'm going to say since it's a two tail test.

The actual 'P' value that I'm going to use is going to be,

this multiplied by two.

Since this is less and my significance level of 0.05,

I would reject the null hypothesis.