Exam Review for Chapters 1_4s1

Exam Review for Chapters 1-4.1 1. Read the paragraph and answer the questions. According to the Kaiser Family Foundation, 84% of U.S. children ages 8 to 18 had Internet access at home as of August 2009. Researchers wonder if this percentage has changed since then. They survey 500 randomly selected children ages 8 to 18 and find that 430 of them have Internet access at home. The foundation concludes that today, the population proportion of U.S. children ages 8 to 18 who have Internet access at home is between 0.830 and 0.890 with a significance level of 0.05. A. Is the first sentence reporting population or sample data? Who is in this group? B. What is the research question? C. Is the third sentence reporting population or sample data? Who is in this group? D. Classify each number in the first 3 sentences as either a parameter or a statistic. Report each with their proper symbol. E. One of the researchers calculates 430 / 500 = 0.86 . What symbol should the researcher use with this number? Why? F. Is the third sentence reporting descriptive or inferential statistics? Explain. G. Is the 4 th sentence reporting descriptive or inferential statistics? Explain. H. Convert the 4 th sentence to an inequality using the proper notation. I. Can the foundation report that the percentage has changed and is now different from 84%? 2. Read the paragraph and answer the questions. National scores for a college math proficiency exam have a bell-shaped distribution with a mean of 80 and a standard deviation of 20. After studying scores from the University of J., educators conclude with 99% confidence that the mean score for UJ students is between 77.2 and 78.4. Their results were based off of a random selection of 150 UJ students who had a mean of 77.8 and a standard deviation of 3.0. Are the educators correct in concluding that the UJ mean is lower than the National mean? A. What is the research question? B. Is the first sentence reporting population or sample data? Who is included in this group? C. Is the 2 nd sentence reporting population or sample data? Who is included in this group? D. Is the 3 rd sentence reporting population or sample data? Who is included in this group? E. Identify each of the numbers in the paragraph as parameters or statistics and report each with the proper symbol and with an inequality if needed. F. Which sentences report descriptive statistics? Which sentences report inferential statistics? G. Based on the reporting, how reliable are the results of the inquiry? What conclusion may be drawn? H. Statisticians know that samples should be similar to the population from which they are drawn. Should consumers of this study be worried that the standard deviation for the UJ students was only 3? I. In fact, consumers of this study ran a statistical test on the standard deviation. If a sample of size 150 random students has a standard deviation of only 3, then with 99% confidence the population standard deviation should be between 2.3 and 4.1. Does it seem that something is wrong with the UJ numbers?

3. What branch of mathematics makes us able to draw conclusions about populations when we only have sample data? 4. State what each symbol represents. If there is more than one possible answer, include all answers. A. x B. ^ p C. σ 2 D. p E. x F. σ G. ρ H . μ I. s J. s 2 K. N L. r M. n 5. Classify the variables as qualitative or quantitative. If possible, classify the variables as discrete or continuous. A. Type of dwelling B. Grade level in School (8 th , 9 th , etc.) C. Year of Birth D. Lightbulbs used in a year E. Zip Codes F. Amount of milk remaining in the carton G. Education level H. Indoor Temperature 6. Convert the sentences to inequalities. Use proper notation. A. The sample mean was greater than 30. B. The sample proportion was less than 0.7 C. The population variance was between 4.7 and 15.5 7. Conversions: A. Convert the sentence to both a proportion and a percentage: The sample contained 1064 random households and 495 owned a dog. B. Convert the sentence to a proportion: In 2020, 31.3% of households in the U.S. owned a cat. Next, calculate how many households owned cats if the population of the U.S. is 328,877,386. 8. A random sample of retired persons recorded the age at which they retired from their career. 62 61 63 62 65 60 62 25 33 60 61 59 62 61 64 60 61 62 63 61 i) Fully describe the shape of the distribution. Support your answer with both a histogram and a box plot. ii) For the data set, calculate the mean, median, and the mode by hand (do not use StatCrunch). Report with proper symbols. Interpret all of these numbers. iii) How do the mean and median support your conclusion about the shape of the distribution? iv) Explain why the relationship between the mean and median exists. v) Calculate the range by hand. Vi) Calculate both the standard deviation and the variance (please use StatCrunch!). Report with proper symbols and interpret both of these numbers. vii) For this data set, what are the best choices of measurements for center, dispersion, and relative position? 9. During the exam, you will not have access to StatCrunch. Instead of having you calculate standard deviation and variance in StatCrunch, you will receive questions similar to the following: A. Given the computer output, find both the standard deviation and the variance if the data set was the ages of all supreme court justices this year. Column Std. dev. Unadj. std. dev. Supreme Court Justice Ages 5.284748 9 4.94343