Question

Some students are good in mathematics and others are better at reading or writing. The question is whether there is any relationship between a student’s ability in math and his/her ability in reading or writing. The SAT, a standardized test for college admissions that is widely used in the United States, has three sections, Math, Critical Reading, and Writing. The table below contains SAT Math, Writing, and Critical Reading test scores for 20 randomly chosen students accepted by a university.

Math Writing Reading

440 410 410

550 570 520

520 520 540

420 470 410

550 620 530

650 560 560

610 620 550

610 520 600

340 470 400

600 540 620

680 580 580

440 430 470

440 450 370

390 430 390

460 600 600

460 520 500

520 570 580

540 530 570

420 430 470

550 480 530

Copy and Paste your data into stat crunch. Label each column.

Create a scatter plot for the Math Scores (x) and Writing Scores (y). Go to statregressionsimple linear. Select x and y and “compute” click the arrow at the bottom to see the scatter plot. Copy a paste a screen shot of your scatter plot

Repeat Step 2, but create a scatter plot for Math Scores (x) and Reading Scores (y). Copy and paste a screen shot of your scatter plot.

Looking at the two scatter plots, which appear to be more strongly correlated, Math and Writing or Math and Reading? Explain.

Compare the r-values for Math and Writing to the r-value for Math and reading. Which appear to be more strongly correlated Math and Writing or Math and Reading? Explain how you can tell using the r-values.

A survey of 300 union members in New York State reveals that 80 favor the Republican candidate for governor. Using the steps below, construct the 90% confidence interval for the true population proportion of all New York State union members who favor the Republican candidate.

A) Find the critical value Zstigma/2 " that corresponds to a 90% confidence level.

B) Find the sample proportion of union member who favor the Republican candidate.

C) Calculate “E”

D) Construct your confidence interval.

E) Write a sentence that explains the meaning of the confidence interval.

I am 90% confident that…..

Answer 1

The scatter plot for the Math Scores (x) and Writing Scores (y) is:

The scatter plot for Math Scores (x) and Reading Scores (y) is:

Since the data for Math Scores (x) and Reading Scores (y) is more clustered, we can say that they appear to be more strongly correlated.

The R-values for Math and Writing to the r-value for Math and reading are 0.68 and 0.78 respectively. Since the r-value for Math and reading is more, they appear to be more strongly correlated.