00:01
So for this problem, for part a, we can see that there is no inherent pairing between samples.
00:22
So it is going to be appropriate to use the independent samples t test.
00:31
For part b, the null hypothesis would be that the mean value for the direct purchases, or the direct investments, would be equal to the mean value for the broker investments.
00:48
And the alternate hypothesis here would be that the mean value for direct is greater than the mean value for the brokers.
00:56
For part c, finding the test statistic, we have that the t value is going to be x bar 1 minus x bar 2 divided by the pooled standard deviation times the square root of 1 over n1.
01:14
Plus 1 over n2, where the pooled standard deviation is equal to the square root of n1 minus 1 times s1 squared plus n2 minus 1 times s2 squared divided by n1 plus n2 plus n2 minus 2.
01:41
So in order to find our pooled standard deviation, we'll need to find first our sample standard deviations.
01:49
For s1, oh, actually, before we get to our sample standard deviations, we're going to need to find our sample mean values.
01:59
So, for x bar 1, we'd find that by taking the sum of all the individual values.
02:08
So 9 .33 plus 6 .94 plus dot, dot, dot, up until that final value of 12 .61, divided by the number of values.
02:18
So we divide by 6, which gives us x bar 1 equals 11 .326.
02:24
Similarly for x bar 2 we add up all the individual values so we'd have 3 .24 plus negative 6 .76 plus dot dot dot up until the final term would be plus negative 0 .13.
02:42
Again divide by 6 and we'll have that that is equal to 3 .83.
02:52
Additionally we have that s1 squared is going to be equal to 1 over the sample size minus 1.
03:00
Times the squared difference between each individual return value and the mean value for that group...