A market researcher selects a large sample of potential car buyers. For each consumer, she records gender, age, household income, and automobile preference. Which of these variables are categorical and which are quantitative? 1.175 Two distributions. If two distributions have exactly the same mean and standard deviation, must their histograms have the same shape? If they have the same five-number summary, must their histograms have the same shape? Explain. 1.176 Norms for reading scores. Raw scores on behavioral tests are often transformed for easier compari- son. A test of reading ability has mean 70 and standard deviation 10 when given to third-graders. Sixth-graders have mean score 80 and standard deviation 11 on the same test. To provide separate "norms" for each grade, we want scores in each grade to have mean 100 and stan- dard deviation 20. (a) What linear transformation will change third-grade scores x into new scores new = a + bx that have the desired mean and standard deviation? (Use b> 0 to preserve the order of the scores.) (b) Do the same for the sixth-grade scores. (c) David is a third-grade student who scores 72 on the test. Find David's transformed score. Nancy is a sixth-grade student who scores 78. What is her transformed score? Who scores higher within his or her grade? (d) Suppose that the distribution of scores in each grade is Normal. Then both sets of transformed scores have the N(100, 20) distribution. What percent of third-graders have scores less than 75? What percent of sixth-graders have scores less than 75? 1.177 Use software to generate some data. Most statis- tical software packages have routines for generating val- ues of variables having specified distributions. Use your statistical software to generate 30 observations from the N(25, 8) distribution. Compute the mean and standard deviation and s of the 30 values you obtain. How close are x and s to the μ and o of the distribution from which the observations were drawn? Repeat 19 more times the process of generating 30 observations from the N(25, 8) distribution and recording x and s. Make a stemplot of the 20 values of and another stemplot of the 20 values of s. Make Normal quantile plots of both sets of data. Briefly describe each of these distributions. Are they sym- metric or skewed? Are they roughly Normal? Where are their centers? (The distributions of measures like x and s when repeated sets of observations are made from the same theoretical distribution will be very important in later chapters.)

A market researcher selects a large sample of potential car buyers. For each consumer, she records gender, age, household income, and automobile preference. Which of these variables are categorical and which are quantitative? 1.175 Two distributions. If two distributions have exactly the same mean and standard deviation, must their histograms have the same shape? If they have the same five-number summary, must their histograms have the same shape? Explain. 1.176 Norms for reading scores. Raw scores on behavioral tests are often transformed for easier compari- son. A test of reading ability has mean 70 and standard deviation 10 when given to third-graders. Sixth-graders have mean score 80 and standard deviation 11 on the same test. To provide separate "norms" for each grade, we want scores in each grade to have mean 100 and stan- dard deviation 20. (a) What linear transformation will change third-grade scores x into new scores new = a + bx that have the desired mean and standard deviation? (Use b> 0 to preserve the order of the scores.) (b) Do the same for the sixth-grade scores. (c) David is a third-grade student who scores 72 on the test. Find David's transformed score. Nancy is a sixth-grade student who scores 78. What is her transformed score? Who scores higher within his or her grade? (d) Suppose that the distribution of scores in each grade is Normal. Then both sets of transformed scores have the N(100, 20) distribution. What percent of third-graders have scores less than 75? What percent of sixth-graders have scores less than 75? 1.177 Use software to generate some data. Most statis- tical software packages have routines for generating val- ues of variables having specified distributions. Use your statistical software to generate 30 observations from the N(25, 8) distribution. Compute the mean and standard deviation and s of the 30 values you obtain. How close are x and s to the μ and o of the distribution from which the observations were drawn? Repeat 19 more times the process of generating 30 observations from the N(25, 8) distribution and recording x and s. Make a stemplot of the 20 values of and another stemplot of the 20 values of s. Make Normal quantile plots of both sets of data. Briefly describe each of these distributions. Are they sym- metric or skewed? Are they roughly Normal? Where are their centers? (The distributions of measures like x and s when repeated sets of observations are made from the same theoretical distribution will be very important in later chapters.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

See similar textbooks