00:01
Let me take note the given values here.
00:02
First of all, the proportion value given as 71%, so we can write as 0 .71.
00:07
And the sample size given here 199.
00:10
And the number of just customer we're satisfied, which is 152.
00:16
So we have to find the test statistic value and the p -value here.
00:20
First of all, the first thing i'm going to find the sample proportion.
00:23
The sample proportion, let's denote by p -hat, which is x over n.
00:29
This is 152 divided by 199.
00:32
152 divided by 199, which would be 0 .76 and 4.
00:38
So let me just state the hypothesis here.
00:41
So the null hypothesis, there is no any difference.
00:44
So that means the p -value is equal to 0 .71.
00:47
And the alternative hypothesis say the b is not equal to 0 .71.
00:51
Because of that, we're going to use a two -tailed test.
00:55
So the first of all, i'm going to find the test statistic value.
00:59
So for the proportion, the test statistic value, which is the z -value here in the formula, this is p -hat minus p divided by square root of p times 1 minus p and divide by n.
01:10
So the p -hat is 0 .764 minus 0 .71 divided by square root of 71 times 1 minus 71, 0 .29.
01:20
And the sample size is 199.
01:22
0 .764 minus 0 .71, which is equal to this number.
01:30
And i'm going to divide this number by the square root of 0 .71 times 0 .29 and divide by 199.
01:36
So the value is 1 .679 here.
01:42
So the next thing, let me just find the p -value.
01:45
Let me draw the normal distribution.
01:46
This is the z -value, 1 .679...