This chart recently appeared in the Los Angeles Times in conjunction with a story describing the poor performance of American high school students in the areas of math and science when compared to similar students from other countries. Students in general take the math and science literacy test, but only college-bound students take the advanced mathematics and physics tests.

To ease your calculation burden: if you treat the mean scores for each country for each test as a sample, the SD for the scores for the three tests are 46.2 for the Mathematics and Science Literacy Test, 34.6 for the Advanced Mathematics Test, and 43.9 for the Physics Test. The means for the three tests are given in the chart.

Assume for the questions below the scattergrams are football shaped.

a. random draws with replacement out of the box containing math and science literacy scores from students in their final year of secondary school as it exists in the world

b. random draws with replacement out of the box containing averages for countries where these tests are administered

c. averages from 21 countries, and they may or may not be all of the elements in the box of means from countries where these tests were administered

d. random draws with replacement out of the box containing scores from students from the 21 countries only

e. either b or c

a. The probability that their deviation from the international average is consistent with chance variation is probably greater than 5%

b. The probability that their deviation from the international average is consistent with chance variation is probably smaller than 5%

c. The size of difference is not big enough to matter

d. There is no difference between these scores and the average that we can attribute to true differences in the population the sample is drawn from

e. There is no difference in scores among these six countries, except for bias

a. The LA Times made a typo (a mistake) in making this table and the real Australia mean score is probably 515

b. The SE for the average for Austria must be smaller than it is for Australia

c. It's most likely a rounding or statistical error, as the footnote indicates

d. The sample size for Austria is probably smaller than it is for Australia but the SD is bigger

e. The Australian sample has more bias, which is taken into consideration in the statistical test

a. There is more variation in Mathematics and Science Literacy scores because there are more countries included in the table

b. When samples are drawn twice from a population in the same manner, you would expect a high correlation between measurements of two similar constructs but when two samples are drawn with different methods from the same population, even if measured on the same construct with the same instrument, the correlation may be low, high, or somewhere in between

c. It is probably due to random variation

d. It is a rounding or statistical error, as suggested in the footnote

e. There is less variation in Mathematics and Science Literacy scores because the sample is bigger and so the estimate is more accurate and thus the correlation is smaller

a. 488, same as its Physics score because the means of the two tests are the same

b. 491, or .3 SD below the mean, because Latvia is .3 SD below the mean on the Physics Test

c. 496, or .144 SD below the mean, because Latvia is .3 SD below the mean on the physics test and the correlation between the two tests is 0.48

d. 501, the average of the averages, because in the absence of any other information our best guess is the mean

e. you can't really make a guess if the information is completely missing like this

a. 0.125

b. p = .05

c. impossible to calculate because the tests are different

d. it has to be close to 1.0 because once the U.S. performed poorly on one test, it virtually guaranteed poor performance on the others

e. around 0.5