00:01
Okay, so to answer a, we're gonna do two sample z -tests for the difference in proportions.
00:07
Here the new hypothesis is that there is no difference in the proportion of people agreeing to volunteer between the prediction request and request -only groups.
00:18
P1 equals p2.
00:21
The alternative is that there is a difference in the proportion of people agreeing to volunteer between the prediction request and request -only groups.
00:32
P1 not equal to p2.
00:35
Well, okay, so the z -test for two proportion is calculated using the formula p1 minus p2 over square root of p times 1 minus p times 1 over n1 plus 1 over n2.
00:56
Now here p1 and p2 are the sample proportion from the two groups.
01:05
So pi equals xi over ni.
01:11
And n1 and n2 are the sample sizes of the two groups.
01:16
P is the pooled proportion, which is x1 plus x2 over n1 plus n2.
01:25
Okay, now we can plug in the figures that is given.
01:31
So p1 is equal to 22 over 46 minus 2 over 46, that's p2, square root of p .22 plus 2 over 46 plus 46 times 1 minus 22 plus 2 over 46 plus 46 times 1 over 46 plus 1 over 46.
02:10
And this z value turns out to be 4 .749.
02:19
And the p -value associated with this z -statistic is equal to 2 .048 times 10 to negative 6.
02:51
Now, for a typical test, we can use the significance level of 0 .05.
02:58
Now, since the p -value is less than 0 .05, this means we reject the new hypothesis.
03:05
So, this result affirms that the difference in the proportion of people agreeing to volunteer between the prediction request group and the request -only groups is statistically significant, as the p -value is way less than the significance level of 0 .05.
03:35
So, research options.
03:37
So, one, the large number of individuals in the prediction request group who said they would volunteer versus the actual volunteers in the request -only group suggests people might overestimate their willingness or ability to volunteer when asked to predict.
03:55
But actual behavior for the prediction group wasn't directly observed for volunteer fulfillment.
04:00
So, the difference in agreement rates suggests that the predictions do influence behavior, with those making predictions more likely to agree to volunteer, potentially due to a commitment effect or a psychological desire to remain consistent with their prediction...