|
Question 557949: A person scores 81 on a test of verbal ability and 6.4 on a test of quantitative
ability. For the verbal ability test, the mean for people in general is 50 and the standard deviation is 20. For the quantitative ability test, the mean for people in general is 0 and the standard deviation is 5. Which is this person’s stronger ability:
verbal or quantitative? Explain your answer to a person who has never had a
course in statistics.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! score is 81 on verbal and 6.4 on quantitative.
mean for verbal is 50 and standard deviation is 20.
mean for quantitative ability is 0 and standard deviation is 5.
strongest would be how the person does relative to the other people.
when the mean is 50 and the standard deviation is 20, then a score of 81 would be equal to (81-50)/20 = 1.55 standard deviations above the mean.
when the mean is 0 and the standard deviation is 5, then a score of 64 would be equal to (6.4-0)/5 = 1.28 standard deviations above the mean.
this person's stronger ability is verbal.
what i calculated was the person's z-score for each of the tests.
the higher the z-score, the more people have a score less than that and the less people have a score greater than that.
if your were able to look up the z-score in a table, you would find that:
with a z-score of 1.55, 94% of the people taking the test would have scores less than that and only 6% would have scores greater than that.
with a z-score of 1.28, 90% of the people taking the test would have scores less than that and only 10% would have scores greater than that.
he did good in both tests, but he scored better than the general population in the test of verbal ability.
|
|
|
| |
