00:01
For this problem, we have that our null hypothesis is going to be that the proportion of support for the death sentence among college students is equal to that of the general american population, 0 .55.
00:19
The alternate hypothesis is that it is lower.
00:24
So we have the alternate hypothesis, p less than 0 .55.
00:28
To find our test statistic, it's going to be a z -score, which is equal to our sample proportion minus the null hypothesized proportion, divided by the square root of p0 times 1 minus p0, divided by n.
00:45
Our sample proportion, p -bar, is going to be equal to 480 out of 968, which gives a result of 0 .496.
00:56
So, plugging in all of our values, we have 0 .496 minus 0 .55, divided by the square root of 0 .55 times 0 .45, over 968, which gives us a z -score equal to negative 3 .38, roughly.
01:16
Now, i'll note that the p -value is going to be the proportion of the standard normal distribution to the left of our observed value at negative 3 .38.
01:25
So i'll find that using a table of values up here.
01:28
So we have negative 3 .38, there, gives us a p -value of 0 .004...