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

13. Joel records the number of hours he gets each night and includes the following table in his report: Number of hours 4- 5 6-7 8-9 10-11 Number of nights 1 3 4 1 A. What is the modal class? B. What is the frequency of the modal class? C. What is the relative frequency of the modal class? D. For how many nights did Joel record his sleep? E. What is the lower class limit of the 2 nd class? F. What is the midpoint of the 2 nd class? G. What is the class width? H. What are the best measures of center, dispersion, and relative position for this data set? 14. A Histogram is given. A. What is the modal class? B. What is the frequency of the modal class? C. What is the relative frequency of the modal class? D. How many data values are in the data set? E. What is the lower class limit of the 2 nd class? F. What is the midpoint of the 2 nd class? G. What is the class width? H. What are the best measures of center, dispersion, and relative position for this data set? 15. What is the only measure of center that may be used with qualitative data? 16. Match the measure with its advanced information I. Reports the number of standard deviations a data value is from the mean a. Mean II. Reports the percentage of data values that are greater than the mean b. Range III. The square of the standard deviation c. Variance IV. The square root of the standard deviation d. Median V. An average of the distance one data value is from the median e. Inter quartile VI. Separates the middle 50% of data values from the rest of the data values Range

VII. Reports the percentage of data values that are less than or equal to the mean VIII. The most frequent data value f. Z-scores IX. Separates the data values into groups of 25% g. Percentiles X. Separates the lowest 50% of data values from the highest 50%. h. Mode XI. Measures the full length of the data set. i. Standard XII. The balance point of the data set. Deviation XIII. The center of the data set j. Quartiles XIV. Measures the length of the middle 50% of data values. XV. Reports the number of data points a data value is from the mean. XVI. An average of all the distances the data values are from the mean 17. Which measure/s of center suffer from a massive loss of information? Which measure/s of center may be used with qualitative data? Which measure/s of dispersion suffer from a massive loss of information? Which measure/s of dispersion are resistant? 18. How can a measure be tested for resistance? 19. Name 3 measures of center. Name 4 measures of dispersion. Name 3 measures of relative position. 20. What must be true if the dispersion of a data set is 0? 21. The lengths of adult male marmosets are normally distributed with a mean of 20 cm, and a standard deviation of 0.6 cm. a) Approximately what percentage of adult male marmosets are longer than 18.2 cm? b) Approximately what percentage of adult male marmosets are shorter than 19.4 cm? c) What lengths are usual for adult male marmosets? d) If an adult male marmoset has a length of 18.6 cm is this unusual? e) Calculate the z-score for an adult male marmoset who has length of 21 cm. Interpret this z-score. Does this z-score indicate an unusual length? Explain. f) Calculate the length of an adult male marmoset who has a z-score of –2.142. 22. Mila records the number of hours of sleep she gets each night and includes the following table in her report: Number of hours 5 6 7 8 Number of nights 3 2 5 9 Calculate the mean hours of sleep Mila is getting per night. For how many nights did Mila record her sleep? 23. The mean of the z-scores is always ______________. The standard deviation of the z-scores is always ________________. What z-scores indicate unusual data values? 24. The GRE is an exam that some students need to take before Graduate School. The mean score on the verbal section of the GRE is 150 points, with a standard deviation of 8 points. The analytical writing section of the GRE has a mean of 3.5 and a standard deviation of 0.6. Gerhard took the GRE and scored 145 points on the verbal section and 3 points on the writing section. On which section did he perform relatively better? Gerhard scored 160 points on the quantitative portion of the GRE. Interpret the fact that this score of 160 was at the third quartile. 25. Sketch each of the 4 shapes we have learned for distributions.

28. A coffee shop wants to sell a blended coffee. The blended coffee will be 50% Supreme and 10% Dark, and 40% Chocolate flavor. If the Supreme coffee costs $10.50 per pound, the Dark coffee costs $11.00 per pound, and the Chocolate flavor coffee costs $9.00 per pound, what is the average cost of the blended coffee? 29. Decide about the strength and direction of the relationship between the variables by inspecting the scatterplot. Approximate the value of r for each graph. 30. In the linear equation y = 3 − 2 x , what is the slope? What is the y-intercept? 31. A motorcycle shop wants to know if the number of parts ordered is related to the number of calls that they receive. a) What variable should be explanatory, and what variable should be the response? b) The motorcycle shop randomly selects 10 days and records for each day both the number of calls received and the number of parts ordered. Their college student employee calculates that r 2 = 0.882 . Interpret this number. c) Calculate the value of the correlation coefficient. Is there a significant linear relationship between the number of calls they receive and the number of parts ordered? d) The owner of the motorcycle shop wants to tell his other employees that more calls will result in more parts ordered so that the employees will be more active on the shop’s social media sites. What should the college student say?

32. A dietician would like to predict peoples body mass index from the percentage of body fat that is reported with the bioelectrical impedance analysis. a) What variable should be explanatory, and what variable should be the response? b) She selects 12 of her patients and records both their body mass index and the percentage of body fat reported with the bioelectrical impedance analysis. She runs a linear regression and receives the following summary: Simple linear regression results: Dependent Variable: %Fat Independent Variable: BMI %Fat = -14.153669 + 2.0733879 BMI Sample size: 12 R = 0.94299022 R-sq = 0.88923056 Estimate of error standard deviation: 2.7257346 Use the results to answer the questions i) What is the value of the correlation coefficient? Interpret this number. ii) What is the percentage of explained variation? Interpret this number. iii) Is there a significant linear relationship between the body mass index and the percentage of body fat? 33. What are all the possible values for the correlation coefficient? Interpret these numbers. 34. Is the correlation coefficient resistant? What does this mean to you as a researcher? 35. What is the lowest value of the correlation coefficient that will allow us to conclude that a significant linear relationship exists when the sample size is 8? 36. Why should you always inspect a scatterplot of the data before running a linear regression? 37. Why is correlation not the same as causation? 38. If a random sample of 9 data points shows a possible linear trend with no outliers and r=0.6, does the sample support a significant linear relationship? If a random sample of 16 data points shows a possible linear trend with no outliers and r=0.5, does the sample support a significant linear relationship?