00:01
Let me take note the given values.
00:02
First of all, the sample size denoted by n, that was given as 96, and the number of people who indicate that they preferred outdoor exercise, which is 65, and the confidence level here given as 99 percent as a decimal number we can write as 0 .99.
00:20
So what do we have to find? we have to find the margin of error.
00:23
Remember the margin of error for the proportion.
00:26
So the margin of error for the proportion, which is this is the z alpha over 2 times the square root of, this is p hat times 1 minus p hat and divided by n.
00:38
So what is p hat? so p hat is the sample proportion.
00:41
Let me get the sample proportion value first.
00:43
This is x over n, which is 65 divided by 96.
00:47
So this is 65 divided by 96 would be which is 0 .677.
00:55
In the next step, let's get the z value here.
00:57
So the alpha is 1 minus confidence level, but we need alpha over 2.
01:01
This is 1 minus 0 .99 and divide by 2, which would be 0 .005.
01:06
To get the z alpha over 2 value, i'm going to use the graphing display calculator application at this step, which is 0 .005, the mean and the standard deviation...