Foundations of Statistics Sophia Milestone 1 Complete Solutions With Rationale

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You passed this Milestone 16 questions were answered correctly. 4 questions were answered incorrectly. 1 On a recent news report, Taylor heard that, on average, most Americans get six hours of sl... eep each night. The report continued by stating that in Taylor's state, Minnesota, residents were actually getting an average of eight hours of sleep each night. Considering the information in this news story, which of the following correctly describes a parameter?  The average number of hours residents of Minnesota sleep  The average number of hours people sleep nationally  The total number of people who participated in the study  The total number of people from Minnesota who participated in the study RATIONALE The parameter represents the value of the variable of interest of the population. In this case, the population is all people nationally, so their average number of hours of sleep is the parameter. CONCEPT Classifying Data by Who You are Testing: Statistics and Parameters 2 A new shop owner has a store 0.5 miles from where it is advertised. She read that it takes the average adult 8 minutes to walk a half mile. She decides to test this and wants to obtain a random sample of 200 adults. Which of the following would be her hypothesis?  The time to walk a half mile is 8 minutes.  Most adults will not walk the half mile to her store.  The time to walk a half mile is greater than 8 minutes.  The time to walk a half mile is less than 8 minutes. RATIONALE Since we are only testing whether or not the average time is 8 minutes or not, that is our null hypothesis. CONCEPT Setting up an Experiment 3 You want to figure out if the amount of sleep you get at night helps increase the grade you get on an exam the following day. You decide to record how many hours of sleep you and your friends got before an exam along with the grade you received on that exam. You then plot the results on a scatterplot and find that as the number of hours of sleep goes up, so do the exam grades. You then conclude that increased sleep causes higher exam scores. Is your conclusion necessarily true?  No, because the apparent correlation between sleep and exam scores might be caused by another variable.  Yes, because sleep and exam scores are highly correlated.  Yes, because as the number of hours of sleep increases, so do exam scores.  No, because the number of hours of sleep and exam scores are not necessarily correlated. RATIONALE Recall that just because two variables show a correlation on a graph, it does not mean they are correlated in practicality. It's very possible that other factors cause the increase in grades such as the amount of studying that is done. CONCEPT Cautions About Correlations and Causation 4 As project manager for an online-course design company, Rachel had data that applied to several different course-development methods. When the company began preparing the next course set, Rachel was interested in how development time varied with each method. Determine which graph would have the largest standard deviation.     RATIONALE Standard deviation is a measure of spread of the data so the one with the largest standard deviation would be the widest looking graph. CONCEPT Representing How Data Can Vary 5 Derek recently started a new diet and exercise program. He was curious to know what exercise would help him burn the greatest amount of calories. He asked his friend Mike, who is a personal trainer, for help. During each exercise, Mike recorded the time Derek spent doing an exercise while Derek kept his intensity relatively constant, and they tracked how many calories each exercise burned. Derek and Mike are in effect performing an experiment that contains explanatory and response variables. Which statement best describes the explanatory and response variables involved in this experiment?  Calories burnt is the explanatory variable and exercise is the response variable, because the calories burnt manipulates the type of exercise.  Exercise type is the explanatory variable and calories burnt is the response variable, since each exercise causes Derek to burn calories differently.  Exercise type is the response variable and calories burnt is the explanatory variable, since different exercises will cause more calories to be burnt.  Calories burnt is the response variable and exercise type is the explanatory variable, because Mike measures exercises as he records calories burnt. RATIONALE Derek is assuming that the number calories burned is dependent upon the type of exercise he is performing. Therefore, calories is the response or dependent variable and exercise type is the independent or explanatory variable since it explains the amount of calories Derek burned. CONCEPT Importance of Experiments 6 In a normal distribution, which statement best describes the relationship between mean, median, and mode?  The mean will always be the smallest value, while the mode and median will be the same.  The mean and median will fall in the center of the distribution and the mode will be larger than both.  The mean, median, and mode always are equal to one another and lie in the center of the distribution.  The mode will be in the center of t [Show More]

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