Math 230 Exam 1 Name October 2, 2002

Transcription

1 Math 230 Exam 1 Name October 2, 2002 Instructions:Please read and answer each question carefully. When answering questions, use complete sentences. For full credit, make sure that your answers have statistical support. Good Luck! 1. Data from a medical study contain values of many variables for each of the people who were the subjects of the study. Which of the following variables are categorical and which are quantitative? a) Gender (female or male) b) Age (years) c) Race (Asian, Black, white, or other) d) Smoker (yes or no) e) Systolic blood pressure (millimeters of mercury) f) Level of calcium in the blood (micrograms per milliliter) 2. Environmental Protection Agency regulations require automakers to give the city and highway gas mileages for each model of car. The table below gives the highway mileages (miles per gallon) for 26 midsize 1998 car models (recorded in increasing order for you convenience). MPG a) Make a stem-and-leaf plot. Be sure to choose that the stem that gives an optimum display.

2 b) Using the highway miles per gallon data calculate the five number summary: MPG lo = Q 1 = Med = Q 3 = hi = c) Use the five number summary to build a box plot for this data. (Five points Extra credit for building a modified boxplot (with explanation)) MPG d) Using the graphical displays constructed above, describe the main features (shape, center, spread, outliers, etc.) of the distribution of highway mileage. e) If the government imposes a 'gas guzzler' tax on cars with low mileage, which of these cars do you think are subject to the guzzler tax?

3 3. Women were allowed to enter the Boston Marathon in The times (in minutes, rounded to the nearest minute) for the winning woman from 1972 to 1998 appear below: Year Time Year Time Year Time Below is a timeplot of the winning times Year Give a brief description of the pattern of Boston Marathon winning times over these years. Have times stopped improving in recent years?

4 4. Below is a stemplot of the distribution of the percent of high school seniors who take the SAT in various states. MTB > stem 'Percent' Stem-and-leaf of Percent N = 51 Leaf Unit = (2) a) Briefly describe the overall shape of the distribution. b) Find the midpoint of the data (median) and distinctly mark this value on your stemplot. c) Explain why describing the center is not very useful for a distribution with this shape? d) Based on the data (percent of students in a given state that take the SAT), speculate on why the distribution has this shape.

5 5. A new article reports that of the 411 players on National Basketball Association rosters in February 1998, only 139 "made more than the league average salary" of $2.36 million. Is $2.36 million the mean or median salary for NBA players? Explain! How do you know? 6. Scores on the Wechsler Adult Intelligence Scale for the 20 to 34 age group are approximately normally distributed with µ = 110 and σ = 25. a) Use your knowledge of the normal distribution to sketch the IQ distribution. Be sure to carefully label the horizontal axis. Use your knowledge of the normal distribution and Table A, or your TI-83+, or the accompanying Minitab output to answer the following questions. (If you use Minitab output, circle and label the portion of MTB you used to answer parts (b) - (e).)

6 b) What percent of people age 20 to 34 have IQ scores above 100? c) What IQ scores fall in the lowest 25% of the distribution? d) How high an IQ score is needed to be in the highest 5%? e) Marilyn vos Savant is know for her widely popular column, "Ask Marilyn" which appears in the Sunday magazine Parade. The Guiness Book of Records Hall of Fame lists Marilyn's IQ as 228 (reportedly the highest ever recorded). What percent of people have an IQ higher than Marilyn's based on this distribution?

7 MTB > cdf 100; x P( X <= x) MTB > cdf 110; x P( X <= x) MTB > invcdf.75; P( X <= x) x MTB > invcdf.25; P( X <= x) x MTB > invcdf.05; P( X <= x) x MTB > invcdf.95; P( X <= x) x MTB > cdf 228; x P( X <= x)

8 6. In each of the following situations, is it more reasonable to simply explore the relationship between the two variables (called the case of no natural structure in class) or to view one of the variables as an explanatory variable and the other as a response variable (called the case of natural structure in class)? In the latter case, which is the explanatory variable and which is the response variable? a) The amount of time a student spends studying for a statistics exam and the grade on the exam. b) The weight and height of a person. c) The amount of yearly rainfall and the yield of a crop. d) A student's grades in statistics and in French. e) The occupational class of a father and of a son. 7. One reason to invest abroad is that markets in different countries don't move in step. When American stocks go down, foreign stocks may go up. So an investor who holds both bears less risk. That's the theory. Now we read that "The correlation between changes in American and European share prices has risen from 0.4 in the mid-1990s to 0.8 in 2000." Explain to an investor who knows no statistics why this fact reduces the protection provided by buying European stocks.