Question
please help me to solve this problem......... im unable to understand it......
To verify whether a course in Research Methodology improved performance, a similar test was given to 12 participants before and after the course. The original marks and after the course marks are given below:
Original Marks   44   40   61   52   32   44   70   41   67   72   53   72
Marks after the course   53   38   69   57   46   39   73   48   73   74   60   78
Was the course useful? Consider these 12 participants as a sample from a population.

From this set of data, we get the following:

The number in each is 12.
The sum of the 1st set is 648 and of the second set is 708.
The sum of the squares of the 1st set is 37,168 and of the second set is is 44,022.

That leads to standard deviations of 14.1 and 14.3.
Based on the difference between the two values,
there is no significant difference between these two.

The average of the 1st set is 54 and the average of the 2nd set is 59.
This gives a difference of 59 - 54 = 5.  That is only around a third of a standard deviation, and that shows no difference between them.

To be exact, I got the following
There area 12 numbers in each set.
The sum of the 1st is 648 and the sum in the 2nd is 708.
The sum of squares in 37,168 in the 2nd is 205.

The average is 54 versus 59.
The variance is 197.8 and 204.5, and those two are too close to be considered different.
This gives standard deviations of 14.1 and 14.3.
With a standard deviation of a little more than 14, and a difference between them of only 5,
they can't be said to be statistically different.
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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.