Colin has computed the variance for his 10 raw scores and obtained = 16.37.He then computed $S_{X}^{2}$ $S \bar{X}$ as follows: $s \bar{x}=\sqrt{\frac{4.046}{10}}=0.636$ What is wrong?
A)Colin first took the square root of $S_{X}^{2}$ and put this into the formula for $S \bar{X}$ .He should have used the $S_{X}^{2}$ = 16.37 value.
B)Colin should have divided here by N - 1.
C)Colin should not have taken the square root of 4.046/10 because he needs $S_{X}^{2}$ in the formula for the t-test.
D)There is nothing wrong with the way Colin has done this problem.

Question

Quizplus · Accepted Answer

A) Colin incorrectly took the square root of the variance ($S_{X}^{2}$) before inserting it into the formula for the standard error of the mean ($S \bar{X}$). The correct approach is to use the variance ($S_{X}^{2} = 16.37$) directly in the formula for $S \bar{X}$, which is $\sqrt{\frac{S_{X}^{2}}{N}}$, without taking the square root of the variance first.

Colin Has Computed the Variance for His 10 Raw Scores SX2S_{X}^{2}SX2​

Colin Has Computed the Variance for His 10 Raw Scores $S_{X}^{2}$