00:01
For this problem, we will be using a chi -squared test for standard deviation or equivalently a chi -squared test for variance.
00:12
The null hypothesis is that the standard deviation is greater than or equal to half an ounce per bottle, 0 .5.
00:29
The alternate hypothesis is the claim that it is indeed less than 0 .5.
00:35
The way that we'll test this is using a chi -squared statistic, which is, the formula is chi -squared equals n minus 1 times sample variance divided by the hypothesized population variance.
00:55
So plugging in the given values, we have, let's see here, 23 times 0 .54 squared divided by 0 .5 squared.
01:09
So we get a chi -squared statistic of 26 .83, roughly.
01:19
And i'll note that the number of degrees of freedom here will be equal to n minus 1, so that's going to be 23 degrees of freedom.
01:26
And we have that the p -value, in this case, is going to be 1 minus the proportion of the chi -squared distribution with 23 degrees of freedom to the right.
01:43
Oh, actually, i'll put it this way...