MATH 1500 Foundation_of_Statistics_Final_Milestone_2020 | Sophia_Learning_Foundation_of_Statistics_Graded A

MILESTONE Score 22/25 You passed this Milestone 22 questions were answered correctly. 3 questions were answered incorrectly. 1 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 strong, the direction is negative, and the correlation coefficient close to 1. • The strength is strong, the direction is positive, and the correlation coefficient is close to 1. • Sophia :: Welcome Page 1 of 26 RATIONALE The closer the data looks to a straight line, the stronger the relationship is. A negative relationship is identified when, as one variable decreases, the second variable increases. Also, if the data is pretty linear and shows a decreasing trend, the correlation is close to -1. CONCEPT Using Data to Identify a Relationship Between Variables 2 Gwen was having issues with her laundry detergent. Her whites were not as bright as she wanted them to be, so she decided to change brands. Before she washed her next set of clothes, she made a hypothesis as to the outcome of using a new detergent. Which of the following would be the null hypothesis? • The new detergent will make the clothes whiter than the old detergent. • The difference between the new detergent and the old detergent will be significant. • The new detergent could be better or worse compared to the old detergent. •  There will be no difference between the new detergent and the old detergent. RATIONALE Gwen is not sure that the new detergent will make them brighter or less bright 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 3 Deon was searching through a list of movies on his streaming movie service and wanted to only look at movies that were rated 4 out of 5 stars or higher. There are a total of 150 movies listed. If 20 of those movies have ratings of 4 stars and 10 have ratings of 5 stars, what is the probability that Deon will randomly select a movie with at least a 4-star rating? • Sophia :: Welcome Page 2 of 26 • • RATIONALE For Deon to select a movie with at least 4 stars it means he has to select a movie with either 4 stars OR 5 stars. have a rating of 4 stars and have a rating of 5 stars. Remember that an "OR" probability means we add them: CONCEPT An Introduction to Probability 4 Marco was a genetic anthropologist interested in determining the heights of third grade children in his community to compare to the national average height. To get his data, Marco traveled to several locations across his city and, at each location, gathered 70 different samples of people's heights. Next Marco found the mean height of each of those samples and plotted the sample means. Which graph shows the correct distribution of sample means if the population mean was a height of 100 centimeters? • Sophia :: Welcome Page 3 of 26 • Sophia :: Welcome Page 4 of 26 RATIONALE When you take many samples and plot their means, the mean values of all those sample means will end up being equal to the population mean. Since normal distribution shows the mean at the center of the distribution on the horizontal axis, the population mean must be at the center of the distribution. Since 100 centimeters is the population mean, this graph is the best answer choice. Sophia :: Welcome Page 5 of 26 Working with Data from Multiple Samples 5 Gaurav was conducting a test to determine if the average amount of medication his patients were taking was similar to the national average. He wants to use a 5% significance level for his test to help ensure that his patients do not receive too little or too much medication. If Gaurav were to conduct a test, what probability value would indicate that his null hypothesis (that there is no significant difference between the amount of medication Gaurav's patients are receiving and the national average) would be rejected? • 50.45% • 95.78% • 5.23% •  1.45% RATIONALE If we are considering a 5% significance level, then this means that we are accounting for 95% of the data. If we picture this on a normal distribution curve, we would say that 2.5% of the data in the left tail is not accounted for and 2.5% of the data in the right tail is not accounted for. Therefore, probability values that are below 2.5% or above 97.5% indicate that the null hypothesis should be rejected. This is because if the null hypothesis were true for a 5% significance level, then it is very unlikely that we would get probabilities below 2.5% or above 97.5% by accident. CONCEPT Introduction to Significance Levels 6 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 • Sophia :: Welcome Page 6 of 26 • 22 •  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 7 Which graph correctly matches a probability value with the shaded region between z-scores? •  Sophia :: Welcome Page 7 of 26 Sophia :: Welcome Page 8 of 26 RATIONALE Remember the 68/95/99.7 rule where 68% of the data lies within 1 standard deviation, 95% of the data falls within 2 standard deviations of the mean, and 99.7% of the data falls within 3 standard deviations of the mean. Sophia :: Welcome Page 9 of 26 Standard Normal Distribution 8 Michael checked several car dealerships around town for the make and model he wanted to purchase. He received eight different quotes: $28,345 $26,780 $28,345 $27,785 $29,450 $28,459 $28,700 $29,995 What is the median car price? • $28,459 • $28,482.38 • $28,345 •  $28,402 RATIONALE The median is found by putting the values in numerical order and selecting the middle value. $26,780 $27,785 $28,345 $28,345 $28,459 $28,700 $29,450 $29,995 For an even number the middle two values are averaged. In this case, the two middle values are $28,345 and $28,459 and their average is = $28,402. CONCEPT Calculating the Center of Data 9 Sophia :: Welcome Page 10 of 26 likely to occur? •  -1.54 • 3.10 • 2.58 • -3.33 RATIONALE Since the graph shows a highlighted area from -2 to 2, the possible z-scores must lie within that range. CONCEPT Determining Likelihood of a Mean 10 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? • Sophia :: Welcome Page 11 of 26  Sophia :: Welcome Page 12 of 26 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 11 Sophia :: Welcome Page 13 of 26 sleep a person gets. His null hypothesis was that taking sleeping pills did not have any effect on the amount of sleep a person receives. Ahmad's alternate hypothesis was that taking sleeping pills increases the amount of sleep a person will get. If Ahmad completed his study, which of the following statements would indicate a Type II error? •  Ahmad's results showed that sleeping pills caused people to get more sleep, and in fact sleeping pills and the amount of sleep people were getting did have a positive cause and effect relationship. • Ahmad's results showed that sleeping pills did not affect the amount of sleep participants were getting when in fact sleeping pills were increasing the sleep people were getting. • Ahmad's results showed that taking sleeping pills did increase the amount of sleep people were getting when in fact sleeping pills were not affecting sleep. • Ahmad's results showed that sleeping pills did not affect the amount of sleep participants were getting when in fact there was not a cause and effect relationship between the two variables. RATIONALE Recall that Type II error is when we fail to reject the null when it is false. In this case, if we determined that the pills had no effect on the amount of sleep, when they really did, it would be a Type II error. CONCEPT Type I and Type II Errors 12 Which statement explains what the slope tells you about the variables in this graph? Sophia :: Welcome Page 14 of 26 The graph shows that the longer you live the higher the chance of drug abuse. • The graph shows that there is a positive relationship between life expectancy and years of drug abuse. • The graph shows that for each year of drug abuse life expectancy went up. •  The graph shows that there is a negative 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 13 The data set below represents the heights (in inches) of students in a particular high school class: 71 62 What is the range of the data set? •  14 inches • 73 inches • 8 inches • 12 inches RATIONALE The range is the largest value minus the smallest value. The largest value is 79 and the smallest value is 59. The range is 73 - 59 = 14 inches in this case. Sophia :: Welcome Page 15 of 26 Calculating the Range of Data 14 Which statement is correct regarding confidence intervals? • A confidence interval is used to indicate a sample mean. •  A confidence interval is used to estimate a range of values for the population mean. • A confidence interval is used to indicate how confident a researcher is with a null hypothesis. • A confidence interval is used to determine the standard deviation from a mean. RATIONALE Remember, confidence intervals are used to provide a range to an estimate of a particular population value so they can be used to estimate a range for the population mean. Since we cannot always sample the whole population, we provide an estimate and a range in which it most likely lies. CONCEPT Introduction to Confidence Intervals 15 As project manager for an online-course design company, Rachel had data that applied to several different coursedevelopment 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 smallest standard deviation. • Sophia :: Welcome Page 16 of 26 Sophia :: Welcome Page 17 of 26 RATIONALE Standard deviation is a measure of spread of the data so the one with the smallest standard deviation would be the narrowest looking graph. CONCEPT Representing How Data Can Vary Sophia :: Welcome Page 18 of 26 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 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. • Kelly only chose learners who were already good at statistics to help ensure that errors in the instruction or assessments were identified. RATIONALE If learners have the ability to opt out of a question or survey, this is participation bias. CONCEPT Issues with Performing Experiments 17 Part of Patrick's job as manager of an indoor pool at the local community center was to determine the type of snacks they should offer, what time of day people were most likely to visit the pool, and the day of the week that has the most swimmers. Patrick 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 Patrick's information? • The type of snacks offered •  The time of day people were most likely to visit the pool • The day of the week with the most swimmers • All of the data is best graphed using a histogram Sophia :: Welcome Page 19 of 26 Histograms are best used with interval or ratio variables. The type of snack offered and day of the week are categorical data, not interval or ratio data, so time of day is the best for a histogram. CONCEPT Graphing Data 18 What percent of data does the region shaded in white represent in a normal distribution? • 75% • 100% •  50% • 25% RATIONALE Recall that a normal distribution is symmetrical so if half the graph is shaded it must equal 50%. Sophia :: Welcome Page 20 of 26 Normal Distributions and Probability 19 Derek recently bought a car and was told by the dealer that he should only use premium fuel. The dealer also told Derek that if he did not use premium fuel the car's fuel economy would drop. To see if this was true, over the period of a few months Derek filled his car with three different grades of fuel and recorded how many miles he was able to get out of each tank of gas under similar driving conditions. Derek is in effect performing an experiment that contains explanatory and response variables. Which statement best describes the explanatory and response variables involved in this experiment? •  Fuel type is an explanatory variable and miles driven is a response variable, because changes in fuel cause the car to have different fuel efficiency. • Miles driven is the response variable and fuel type is the explanatory v- - - - - - - Continued