\"An Analysis of the Study Time-Grade Association,\" published in Radical Pedago

Question

"An Analysis of the Study Time-Grade Association," published in Radical Pedagogy in 2002, reported that scores on a standardized test for cognitive ability for a group of over 100 students in an Introductory Psychology course had mean 22.6 and standard deviation 5.0. For the 7 students who reported studying the most for the course (9 hours or more per week), the mean was 17.6 and standard deviation was 2.8.

(a) Calculate the standardized sample mean, using 5 as the standard deviation. (Answer as a decimal of the form -X.XX or +X.XX.)

(b) Recall that values of z between 0 and 1 are quite common; values closer to 1 than to 2 may be considered not unusual; values closer to 2 are borderline, values close to 3 are unusually large, and values considerably greater than 3 are extremely large. Based on the relative size of your z statistic, is there evidence that mean cognitive ability score for those 7 students was significantly lower than for the population of students in the course?
Yes
No

(c) Can we conclude that studying diminishes a student's cognitive ability?
Yes
No

Explanation / Answer

Answer to part a)

Since it is given that the Population mean of 100 people is M = 22.6 & standard deviation = 5

Thus the standardised mean will be 5 only

.

Answer to part b)

Given: For 100 students: M = 22.6 , SD = 5 ....[this detail serves as population detail]

For 7 students : Mean x bar = 17.6 and s = 2.8 ........[this detail serves as sample detail]

.

Since we got the value of Population standard deviation , we can make use of Z score

Z = (x bar - M ) / SD / (n)

Z = (17.6 - 22.6) / (5 /7)

Z = -2.6458

.

The Value Z = -2.65 is more close towards to -3 than -2

Thus it is considered unusually low

And hence we do conclude that YES there is evidence that mean cognitive score for those 7 students was significantly lower than the population of the students in the course

.

Answer to part c)

Thus we can surely conclude that the study diminishes the cognitive ability of the student

YES

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