Check This Out

1. Check This Out

2. In this one class I had I took a sample of scores on a test from 10 students in the class. The scores are here on the left. I asked myself why all the students didn’t get the same score. I know that they all heard the same most excellent lecture  because I saw all of them at the lecture. Well, I calculated the mean of the scores and I found the mean was 72.9 and the standard deviation was 15.84. You can see that 4 of the scores are below the mean and 6 are above. The lowest score is 47 and the highest is 93. The lowest score of 47 has a z score of (47 – 72.9)/15.84 = -1.64. Well, as I thought more about the scores I went and asked each student how much time was spent studying for the test. The pairs are on the next slide.

3. Scatter plots are tricky! These two scatter plots here are of the same data. The top one is too small, but the dots seem to line up fairly well in a straight line. The bottom one certainly suggests time spent in study and score are related in a positive way, but it is not a straight line.

4. On page 47 of the book you can see the formula for the sample covariance. I did that work here. Note the first person had time 40 and score 77. So on this page for the first person I have 1.3 = 40 – 38.7, and 4.1 = 77 – 72.9. You need to multiply the 2 together to get the product 5.33. Do this for each pair of time, score values and add up all the products and divide the result by 9 = n – 1 to get the covariance = 101.0778. This is a positive number so that suggest that the two variables are positively related. The covariance is a numerical way of confirming what we see in the scatter plot – namely that here the variables are positively related. The correlation coefficient takes the covariance and divides by the product of the standard deviations of time and score. The correlation coefficient of .839279 is positive also confirming the positive relationship we see in the scatter plot. Also since the .839279 is closer to 1 than to 0 then we say the relationship is somewhat strong.

5. Let’s say I look at another class and the correlation coefficient was .3254. The positive value suggests the variables are positively related in this example as well. But a .3254 being closer to 0 than to 1 means the relationship is on the weak side. Correlations can be weak or strong. What does this mean? In the example I am wondering why scores are different for different people? I was thinking that time spent studying would be a reason for different scores. Also note that not everyone spent the same time in study. So a positive correlation is an indication that when time spent studying goes up the score goes up. I would feel a great deal better telling you to spend more time with the material if the correlation is strong as opposed to when the correlation is weak. Here is the last point I would make. The stronger the correlation there is between two variables would suggest that the more the time spent studying was over the mean time spent studying would lead to the actual test score being that much greater than the mean score.