Question

Date: Names Directions: You must work with one or two other students on this take-home exam and you may use your textbook. Your work answering Questions 1 and 2 can be shared, but each of you must do your own Question 3, where each of you will pose your own question based on the data. Only one project will be turned for each team, consisting of joint answers for Questions 1 and 2, and as many Questions 3 answers are there are people in your group. Education Data by State, circa 1995. In the table on the back page we have the data from the mid 1990s about how students in each of the 50 states and the District of Columbia perform on the SAT Verbal and SAT Math exams, as well as other information. You will be emailed an excel version of these data. Feel free to use your TI-83/84 Plus to answer these questions. You may use other softwofe as well. In Question 1, I pose and answer a question based on the data, leaving out some of the writter narrative for your team to complete In Question 2, I pose another question and it is your job to answer it thoroughly, using both appropriate displays of data and a written narrative. Use Question 1 as a model for your answer. For Question 3, each of you is to pose a different question (that is similar to Question 2) and then answer it thoroughly, using both appropriate displays of data and a written narrative. 1. /40 pts) Are there noticeable regional differences in the median teacher pay among states? If so, describe the differences. ANSWER: We begin by looking at the summary statistcs, a dotplot, and a boxplot of the median teachers pay across all states Summary statistics: ColumnMean Variance Std. dev. Std. err. Median Range Min Max Q1 Q3 Teacher Pay ($1000) S1 35.890196 38.762502 6.2259539 0.8718079235 24 26.3 50.3 31.5 40.5 30 40 45 sO Teacher Pay (81000) 50 Teecher Hay C1000) Nationwide, the median median teacher pay (not a mistake to repeat the word median twice here) is $35,000. The minimum median teacher pay is in the state of The maximum median teacher pay is of in the state Although one could argue that the distribution is slightly skewed to theーーーーーーーーーーーthe distribution is mostly symmetric, with an IQR ofーーーーーーーーーーーーー, which s just ㄧ-% of the total range of ーーーーーーーーーーーーー The mean median teacher pay iswith a standard deviation of. With a relatives small sample size of N it is hard to say too much more about this distribution In the data, there are two ways we can look at the question of regional differences. We can either look at the salaries based on census region or more simply by breaking down all of the states into two categories: coastal states versus central States. If we look at the census regions first, we get the following summary statistics, dotplots and boxplots. Summary statistics for Teacher Pay ($1000): Group by: Region Variance * Std. dev. . Region # Mean . Std. err. . Median . Min * Max , Q1 . Ranges n * 934 39.889.287 3.047458 1.362864638.2 | ENC 7.1 37.7 448 37.8 40.9 6.48 2 4 31.3 .5455844 1.272792232.2S.4 27.7 33.1 29.5 33.1 ESC 3 47.366667 1.2133333 1.1015141 0.63595947 2 46.148.1 46.1 48.1 MA 47.9 8 32.025 6.4707143 2.5437599 0.8993549331.25 6.8 29.4 36.2 30.1 33.95 6 40.066667 40.210667 6.3411881 2.5887792 39.2517.4 32.9 50.3 35.8 42.9 MTN NE PAC 5 41.22 29.032 5.3881351 2.4096473 39.6 13.8 35.8 49.6 38 43.1 SA 32.4 10.6 26.3 36.9 27 35.1 WNC 7 31.785714 15.481429 3.9346447 1.4871559 WSC429.125 4.7425 2.1777282 1.0888641288 5.2 26.8 32 27.6 30.65 Region WSC SA PAC NE MTN ESC ENC Teacher Pay ($1000) Region WNC SA PAC ESC ENC 40 30 35 Teacher Pay ($1000) Clearly, the median teachers pay varies considerably from census region to census region Identify the five regions with the lowest median median teachers pay. What do these five regions have in common that may explain why they pay teachers general less than states in other census regions? Identify the four regions with the highest median median teachers pay What do these four regions have in common that may explain why they pay teachers general more than states in other census regions? 2. /35 pts) Using Question 1 as a model, answer the following question. Keep your lives simple - only break down the states by coastal of central states Answer this question thoroughly on your own sheets of paper and include appropriate displays of data. Choose displays that illustrate the points you are trying to make, and refer to them in your written narrative. The written narrative should not be longer than two paragraphs Are there noticeable differences among coastal and central states in the percent of students who take the SAT Exam? If so, describe the differences. 3. (/25 pts) Pose a question similar to the question in Question 2. focusing your question the SAT Verbal scores, the SAT Math scores, or the Percent with No High School Diploma, broken down by coastal and central states. Answer this question thoroughily on your own sheets of paper and include appropriate displays of data. Choose displays that illustrate the points you are trying to make, and refer to them in your written narrative. The written narrative should not be longer than two paragraphs. i raker-ı o m e Exam ISpring 17.pat (page /) ﹀. State Education Data circa 1995 Median MeanMeanPercent Percent Teacher Taking SATs Population SAT Coast/Central (1000 Verbal Math State School AL Coast 558 4273 AK Coast 513 47 MTN Central 32.5 WSC 2510 Central Coast Central MTN Coast 3274 Coast SA 495 Coast 473 FL SA Coast Coast 7353 484 Hl PAC Coast MTN Central ENC Central 11,847 ENC Central 5,841 494 WNC IA Central WNC Central 579 ESC Central 3,884 544 12 WSC LA Coast Coast 1,243 498 Coast 6,092 MI ENC Central 565 Central WNC 593 4,658 ESC Coast WNC Central Central WNC Central MTN Central Central 498 NJ MA Coast 505 23.3 Central 499 MA Coast Coast 486 Central он ENC Central 3,301 wSC Central 18.5 Coast 3,204 Coast 12.056 Coast SA Coast 474 WNC Central 574 Centra WSC 495 4930.6 Central 2,000 Central 589 Coast 496 PAC Central 1826 WI ENC Central Central MTN The census regions are East North Central, East South Central, Mid-Atlantic. Mountain, New England. Pacific, South Atlantic, West North Central, and West South Central

Answer 1

1)
minimum is 26300
maximum is 50300

skewed to right { as mean > median}
IQR = Q3 -Q1 = 9000

range = 24000
37.5% of total range of 9000    {9000/24000 = 0.375}

mean = 35890.196
sd = 6225.9539
N = 51