Question

In a large statistics class, the correlation between midterm scores and final scores is found to be nearly 0.50, every term. The scatter diagrams are football-shaped. Predict the percentile rank on the final for a student whose percentile rank on the midterm is a) 5% b) 80% c) 50% d) unknown

Answer 1

Answer:

A) 21%

B) 66%

C) 50%

D) 50%

Step-by-step explanation:

A) We want to find the percentile rank on the final for a student whose percentile rank on the midterm is 5%.

Now, it means we are looking for the value of z on the 5th percentile.

Now from the Z-score percentile normal distribution table i have attached, the value of z on the 5th percentile is; Zx = -1.645

Now, using the regression method, we know that;

Zy = r(Zx)

Where Zy is the score at which the final percentile occurs.

And r = 0.5 from the question

Thus; Zy = 0.5 x -1.645

Zy = - 0.8225

Now looking at the table attached, there is no direct value of -0.8225,and so we pick the closest to it which is -0.8 and it falls on the 21st percentile.

Thus, the percentile rank on the final for a student whose percentile rank on the midterm is 5% would be 21%.

B) We want to find the percentile rank on the final for a student whose percentile rank on the midterm is 80%.

Following same pattern in A above;

From table, Zx = 0.842

And Zy = 0.5 x 0.842 = 0.421

The percentile for this value is approximately 66th percentile.

Thus, the percentile rank on the final for a student whose percentile rank on the midterm is 80% would be 66%.

C)We want to find the percentile rank on the final for a student whose percentile rank on the midterm is 50%.

Following same pattern in A above;

From table, Zx = 0

And Zy = 0.5 x 0 = 0

The percentile for this value is 50th percentile.

Thus, the percentile rank on the final for a student whose percentile rank on the midterm is 50% would be 50%.

D) If the score is unknown, the best bet will be to use a middle percentile of 50%.

It thus follows the same procedure from c above and same answer of 50%.