The sample data table Scores.jmp contains data for the United States from the Third International Mathematics and Science Study, conducted in 1995. The variables came from testing more than 5000 students for their abilities in Calculus and Physics, and are separated into four regions of the United States. Note that some students took the Calculus test, some took the Physics test, and some took both. Assume that the scores represent a random sample for each of the four regions of the United States.

(a) Produce a histogram and find the mean scores for the United States on both tests. By clicking on the bars of the histogram, can you determine whether a high calculus score correlates highly with a high Physics score?

(b) Find the mean scores for the Calculus test for the four regions of the country. Do they appear to be approximately equal?

(c) Find the mean scores for the Physics tests for the four regions of the country. Do they appear to be approximately equal?

(d) Suppose that from an equivalent former test, the mean score of United States Calculus students was 450. Does this study show evidence that the score has increased since the last test?

(e) Construct a 95% confidence interval for the mean calculus score.

(f) Suppose that Physics teachers say that the overall United States score on the Physics test should be higher than 420. Do the data support their claim?

(g) Construct a 95% confidence interval for the mean Physics score.