MATH 300 Foundations of Statistics_Sophia_Milestone 1_2020 | Foundations of Statistics_Graded A

MATH 300 Foundations of Statistics_Sophia_Milestone 1_2020 – Strayer University 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 sleep 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 Parameters2 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 Experiments6 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 the distribution and the mean and median may be higher or lower. RATIONALE In a normal distribution, all the measures of center (mean, median, and mode) are the same and equal to the center value. CONCEPT Representing How Data is Normally Distributed 7 The data on this graph represents the number of sales for several types of vehicles in 2015. Which vehicle represents the mode? • Ferrari LaFerrari• 458 Spider • Enzo • F12berlinetta • Ferrari FF RATIONALE The mode is the value that occurs most often, or has the highest frequency. The tallest bar on this bar chart is 458 Spyder, which indicates the mode. CONCEPT Identifying Measures of Center on a Graph 8 The following data set shows the blood sugar levels (in mg/dL) in a group of 9 patients about to undergo a study of a new drug. What is the interquartile range for this data? • 19 • 22 • 11 • 14RATIONALE Remember the Interquartile Range (IQR) is the third quartile minus the first quartile. Sort the data in ascending order and find Q1 and Q3. Note that the median is 147. Q1 is found by the median of the first 4 values and Q3 is found by the median of the last 4 values. We can find both values by taking the averages in these ranges: So the IQR is equal to: CONCEPT Calculating the Interquartile Range 9 Mike was the director of admissions at a university. He wanted to learn more about the gender of applicants, what majors were most popular, and the age groups of learners applying to the university. Mike wants to create either a bar graph or a histogram for his data. For what data would the histogram be the best way to represent Mike's information? • The gender of applicants • The majors that are most popular • The age groups of learners applying for admission• All of the data is best graphed using a histogram RATIONALE Histograms are best used with interval or ratio variables. The gender of applicants and popular majors are categorical data, not interval or ratio data, so time of day is the best for a histogram. CONCEPT Graphing Data 10 Given the following graph of a skewed distribution, which answer choice best represents how the mean, median, and mode are related? • The median is the largest, followed by the mode, and then the mean. • The mode is the largest, followed by the mean, and then the median. • The mean is the smallest, followed by the median, and then the mode. • The median is the smallest, followed by the mode, and then the mean. RATIONALE This is a left skewed distribution which indicates a low mean and high mode. The peak is towards the right so that is where the mode is, but the values go infinitely to the left so the mean is low. The median is in the middle. CONCEPT Representing How Skewed Data is Distributed 11 If the sum of squares for a sample containing 51 items equals 200, what is the standard deviation?• 1.98 • 3.92 • 4.00 • 2.00 RATIONALE The standard deviation is found by dividing the sum of squares by (n-1) and taking the square root so here it would be: - - - - - - - - Continued