MATH 300 Foundations of Statistics_Sophia_Milestone 1_2021 – Strayer University

MATH 300 Foundations of Statistics_Sophia_Milestone 1_2021 – 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 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 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. 141 158 144 153 139 136 147 155 152 What is the interquartile range for this data? • 19 • 22 • 11 • 14 RATIONALE 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: CONCEPT Calculating Standard Deviation and Variance 12 Kelly designed a new course in statistics and was getting ready to determine how well the course would be received by potential learners. Kelly hoped to gain data on how difficult or easy the course was, as well as how much learners enjoyed the course experience. To get this information, Kelly gathered a few groups of different learners and began her initial tests. Which of the following is an example of participation bias? • Kelly only chose learners who were already good at statistics to help ensure that errors in the instruction or assessments were identified. • Kelly selected a set of learners who were all representative of the typical learner population. • All participants in the initial test had to give responses to survey questions before their data was evaluated. • The learners in the initial test have the ability to respond or not respond on surveys related to the course. RATIONALE If learners have the ability to opt out of a question or survey, this is participation bias.  CONCEPT Issues with Performing Experiments 13 Which statement best describes the strength, direction, and correlation coefficient of the scatter plot shown here? • The strength is strong, the direction is negative, and the correlation coefficient is close to 1. • The strength is weak, the direction is positive, and the correlation coefficient is close to 0. • The strength is strong, the direction is negative, and the correlation coefficient is close to 0. • The strength is strong, the direction is positive, and the correlation coefficient is close to 1. RATIONALE The closer the data looks to a straight line, the stronger the relationship is. A positive relationship is identified when, as one variable increases, so does the second variable.  Also, if the data is pretty linear and shows an increasing trend, the correlation is close to 1. CONCEPT Using Data to Identify a Relationship Between Variables 14 The data set below represents the heights (in inches) of students in a particular high school class: 58 67 62 64 71 55 64 66 74 59 67 62 What is the range of the data set? • 18 inches • 74 inches • 19 inches • 21 inches RATIONALE The range is the largest value minus the smallest value.  The largest value is 74 and the smallest value is 55.  The range is 74 - 55 = 19 inches in this case.  CONCEPT Calculating the Range of Data 15 Michael checked several car dealerships around town for the make and model he wanted to purchase. He received eight different quotes: $22,456  $26,780  $25,430  $24,275 $27,050  $28,459 $24,500 $26,780 What is the mode of the data set? • $25,716 • $26,105 • $26,780 • $24,500 RATIONALE The mode is the value that occurs most often on that list. To find the mode, simply count how often each value occurs.  The only value that appears more than once is $26,780 (appears twice). CONCEPT Calculating the Center of Data 16 Which statement explains what the slope tells you about the variables in this graph? • The graph shows that there is a negative relationship between life expectancy and years of drug abuse. • The graph shows that the longer you live the higher the chance of drug abuse. • The graph shows that for each year of drug abuse life expectancy went up. • The graph shows that there is a positive relationship between life expectancy and years of drug abuse. RATIONALE If one variable decreases as the other variable increases, the two share a negative slope.  Here, as the years of drug abuse increase, the life expectancy decreases, therefore there is a negative slope or relationship between the two. CONCEPT Representing How Two Data Sets are Related 17 Because her current cable provider wasn't providing the service she desired, Gwen decided to change companies. Gwen made a hypothesis as to the outcome of using a new cable provider. Which of the following is the null hypothesis? • There is no difference between the level of service provided by either company. • The new company will be better than the old company. • The new company will be worse than the old company. • The new company may be better or worse than the old company. RATIONALE Gwen is not sure that the new provider will have better or worse service so we always set the null hypothesis to say that there is no difference between the two.   CONCEPT Identifying a Reason for Performing an Experiment 18 Distributions may be normal or they may be skewed to the left or the right.  Which of the following graphs is an example of a left-skewed distribution? • • • • RATIONALE In a left-skewed distribution, the mode will be toward the right and the tail is pointing to the left.  CONCEPT Representing Skewed Data on a Graph 19  This graph shows the frequency of common mechanical issues with 1969 Camaros. What type of data does this graph represent? • Ordinal • Interval • Ratio • Nominal RATIONALE Nominal data provides categories.  It is based on characteristics that do not have direction or magnitude.  When something does not have direction, then the order it’s presented in does not matter.  When something does not have magnitude, then this comparison can’t be made.  So these four issues (or categories) represent nominal data.  Ordinal data also is based on characteristics but they need to be able to be put in a meaningful order.  Interval data provides numbers, so that the difference between two values can be measured.  Ratio data occurs in most types of physical measurements, such as length, width, and weight. CONCEPT Data Comes in Different Types 20 Two drains in Bill's house were clogged. After considering the selection of drain cleaners at the hardware store, Bill chose a brand that claimed to be effective with just one use. Back at home, Bill eventually had to use the cleaner three times before the drains cleared, but he was still satisfied with the product. Which of the following correctly describes the sample? • The products Bill chose • The number of times it takes for Bill's drains to unclog • The number of drains the product's manufacturer tested • All of the different types of drain cleaning products RATIONALE The sample items are the ones that are chosen for the experiment, so in this case it would be the products Bill purchased and used at home.   All the different types of drain cleaning products would be the population, while the number of drains the product's manufacturer tested and the number of times it takes for Bill's drains to unclog would be the parameters and statistics of the experiment.