David was interested about the performance of a sports car, but was confused about scatterplots. Tasha collected some performance data from the internet about the car's engine. Specifically, she plotted the horsepower against the engine speed (in 1000 revolutions per minute). The points fall closely on a line. Using the data values Tasha collected, the slope of the best-fit line is __________. By observing another set of data values, Tasha used a calculator for the tire diameter at the tread and circumference data and got an equation for the least-squares line: = 0.1 + 3.1x. Using this equation to predict circumference from diameter at the tread, the circumference for a 30-inch diameter at the tread tire would be __________. Tasha kept track of the miles she was able to drive versus the gallons of gas in her car's fuel tank. During this time, she always filled her tank completely when she got gas. After filling her tank eight times, she plotted the miles driven on the x-axis and the gallons on the y-axis. If she were to create a scatterplot of her data, the direction of the association would be (A) __________. The strength of the association would be (B) __________. Jesse put the heartbeat and lifespan data into a statistical software program. The software produced a scatterplot of the data, and Jesse noticed the downward trend as he read the graph from left to right. Then he used the software to calculate the coefficient of determination to be 0.64. The value of the correlation coefficient is __________. Simone checked the two anomalous data points and found that they were for reptiles that require more expensive food than the mammals. If Simone removes these two points and then recalculates r, the correlation coefficient (r= 0.7) will (A) __________ (increase, decrease, show no change)? (B) Would these points be considered influential? Jesse took two data points from the weight and feed cost data set and calculated a slope, or average rate of change. A hamster weighs half a pound and costs $2 per week to feed, while a Labrador retriever weighs 62.5 pounds and costs $10 per week to feed. Using weight as the explanatory variable, the slope of a line between these two points is __________. Jesse entered the weight (in pounds) and weekly food cost data (in $) into a statistics software package and found a regression equation of = .3 + .12x. This means that, on average, for each additional (A) __________, the weekly feed cost goes (B) __________ 12 cents. At the clinic where Jesse worked, the weekly feed cost for a rabbit was $2.20. The rabbit used for the study weighed nine pounds. Using the equation = .5 + .16x for the regression line of weekly food cost on weight (weight is explanatory), the residual for the rabbit is __________. Jesse used a regression equation for weight of an animal (explanatory) and weekly food cost (response). Using the regression equation = .3 + .12x, the predicted weekly food cost for a hedgehog weighing 1.3 pounds is __________. The study Shawna read about the weight and calories burned included results in the form of a scatterplot. Looking at the scatterplot, the form is (A) __________. The strength of this correlation can best be described as (B) __________ and r-squared is likely close to (C) __________. The study on calories burned per minute of walking, depending on weight, has a regression equation of = 1.1 + .03x. The predicted number of calories burned in a minute of walking for a 150 pound person is __________. Shawna looked at a study on mortality rates for men and women aged 65 to 74. When the researchers looked at calories of sweeteners consumed per day by women as the explanatory variable, they got a regression equation of = - 40.857 + 0.704x with r = 0.74. The percent of the change in mortality rate that is explained by the change in calories of sweeteners is __________. Shawna knew that a correlation between calories of sweeteners consumed and mortality rates does not, in itself, mean that more sweeteners leads to a higher chance of dying. It's possible that a __________ variable is actually causing a change in both variables. If calories from sweeteners are not the cause of early mortality, Shawna wondered what else might be a factor. Which of the the following methods is best suited, which is least suited to establish causation between the two variables? Order the methods from best suited to least suited. 1. 2. 3. a. retrospective cohort study b. controlled randomized clinical trial c. observational study Shawna read a scatterplot that displayed the relationship between the number of cars owned per household and the average number of insured citizens in neighborhoods across the country. The plot showed a strong positive correlation. Shawna recalled that correlation does not imply causation. In this example, Shawna saw that increasing the number of cars per household would not cause members of her community to purchase health insurance. The likely confounding variable that is causing an increase in both the number of cars and average number of insured citizens is __________. Shawna found a study of American women that had an equation to predict weight (in pounds) from height (in inches): = -260 + 6.6x. Shawna's height was 64 inches and her weight was 150 pounds. The value of the residual for Shawna's weight and height, using this regression equation, is __________. At the idea of surveying their fellow students about their sleeping habits, and comparing this to the general population, Myra began to perk up. \"I remember from my statistics course that we need to start by coming up with a hypothesis. I suspect that full-time college students are chronically sleep deprived, getting less than 8 hours of sleep.\" \"That's a good hypothesis, Myra.\" Jason thought for a minute about their sample. \"Let's call 15 of our friends randomly and see what they have to say about their sleeping habits. Remember that one of the conditions for performing a hypothesis test is that the observations are independent." If they have already sampled 15 students, Jason and Myra will need to sample (A) __________ more students, to assume normality of the test statistic. If Jason and Myra had sampled 40 students without replacement, the minimum population size would have to be (B) __________ to treat the observations as independent. A few days later, Myra and Jason had another late-night studying session to organize their thoughts about the hypothesis test they want to perform. After reviewing their statistics information further, Myra concluded, \"I think it would be meaningful to focus our efforts on examining if students are not getting an average of 8 hours of sleep." What is the null_____? and alternative hypothesis_______?. Myra and Jason continued their study and reviewed their data from, what was now, a sample of 101 students! The survey results show that their sample of students got an average of 6.5 hours of sleep each night with a standard deviation of 2.14. Using a 95% confidence level, they also found that t* = 1.984. A 95% confidence interval calculates that the average number of hours of sleep for working college students is between the lower value of (A) __________ hours and the upper value of (B) __________ hours. \"Myra,\" said Jason, \"this is where my knowledge of statistics is a little weaker than yours. I'm still not sure how we can use this sample to make a statement about the sleeping habits of an entire population of working college students.\" \"Look Jason,\" Myra replied. \"Here is the stack of survey responses. Pick out five of them at random, and then make a list of them on a sheet of paper.\" When Jason was finished, his list looked like this: Subject #12: 6 hours Subject #23: 6.5 hours Subject #49: 6 hours Subject #82: 7 hours Subject #98: 5 hours \"Let's consider these five as the population,\" said Myra. \"Now, all ten samples of the size n = 2 can be taken, and the sample means can be found. For example, the mean of the first two subjects is 6.25 hours of sleep. The Central Limit Theorem tells us that distributions with a finite mean and standard deviation, the distribution of the sample means is approximately normal for large sample size. \" Using the data from the 5 students above, the mean of these sample means is (A) __________, and the standard error of the sample mean is (B) __________. \"So now,\" continued Myra, \"We will proceed to do a one-sample t-test on a group. We'll use a new set of data values. Show me the list of values you get.\" Subject #15: 6.5 hours Subject #27: 5 hours Subject #48: 6 hours Subject #80: 7.5 hours Subject #91: 5.5 hours Jason learned that their t-distribution is similar to the normal distribution but has (A) __________ tails. The value for the degrees of freedom is (B) __________. Jason said, \"I think I'm beginning to understand this better, Myra. We know that the normal adult population gets, on average, 8 hours of sleep each night. Hypothesis testing helps us see if college students are different from the general population.\" \"Right,\" replied Myra. \"You're beginning to see the bigger picture. The t-test is how we'll know if we're dealing with a difference, or not.\" Jason and Myra tabulate that their sample of 101 students got an average of 7.1 hours of sleep each night, with a standard deviation of 2.48. Using the formula and information from their sample, the t-statistic Jason and Myra calculate is __________. \"There's one final thing we need to look at,\" Myra said. \"We don't know the population's standard deviation, although we do know the standard deviation of our sample.\" \"I think I remember this Myra,\" said Jason. \"I can't remember what it's called, but in statistics there's a test that will give us a number that will tell us about how likely it is that the relationship is due to pure chance.\" Myra smiled, knowing that she could count on Jason's grasp of statistics after all. \"That's the p-value, Jason. And once we know what that is, we'll be able to make a decision about our hypothesis.\" Given a p-value of 0.02, and a significance level of 3%, Jason and Myra should __________ the null hypothesis. As Myra and Jason wrapped up the basic statistical analysis of their project, they discussed if their project should consider if sleep deprivation varies across other age groups as well. Myra says \"Let's give our survey to an equal number of kids, teenagers, adults, and senior citizens. Then we'll use the new data to perform an ANOVA test.\" Later on, Myra and Jason decide to simultaneously study the number of hours of sleep across the age groups, as well as their primary residence location (urban, suburban and rural). In this case, they should use __________ as their statistical test