## Statistic Thought Questions

10. At the age of 8, Max obtained an observed score of 48 on a standard test of vocabulary. After a year of
therapy directed at enhancing his vocabulary level, he was retested and obtained an observed score of
60. The test manual indicates that the average 8 year old child obtains an observed score of 60 (SD =
6.0), and the average 9 year old child obtains an observed score of 70 (SD = 4.0). Briefly explain
whether, or not, there is evidence that therapy has been effective at enhancing his vocabulary level.
(Limit the length of your answer to 3 or 4 sentences. Worth 5 marks.)

11. It is widely accepted that a gram of fat has 9 calories, a gram of carbohydrate has 4 calories, and a gram
of protein has 4 calories. Sodium has no calories. If there are no calories in sodium, why is it that, in
question 9b), the correlation between calories and sodium is not equal to zero? (Limit the length of

For Question 10, when calculating the Zscore for Max, would we use the SD for the average child in a population or do we calculate based on the JUST max's data?
I'm thinking that one would calculate the score using the population SD because SD are usually calculated from a group of scores not just one.

Also when you say effective do you mean reach the same level as the average child OR the same increase in score for the vocabulary test?
I calculated the t score and the change from 8 to 9 years old for max is similar to that of a average child.

For Question 11, I was thinking one could argue both the indirect effect and the multiple indicator effect.
which is better to argue?

2. Indirect Effect

Y  Z

X

Improvement in shoes that lead people to run faster
X = years elapsed since prev Olympics
Y = things happen in the time
Z = causing real change in gold medal time

X = Wife
Z = Chris
Y = Dog gets kicked

Wife yells at chris
Chris kicks dog
Indirect effect but X not lead to Y

Change but not direct cause from X to Y
3. Multiple Indicators

Y

X

Check

Both measures of distance
(use different rulers)
Steps vs. meters
Not same exaclty

Temperature
X = Fahrenheit
Y = Celsius
Perfectly correlated

Y and X are the same measure of same underlying concept but in 2 different ways