11.1
What is a Correlation Coefficient?
Be specific!
The correlation coefficient is a statistical measure (r) that quantifies the strength and direction of a linear relationship between two variables, ranging from -1 to +1.
What is the Least Squares Regression Line?
Be specific!
The least squares regression line is a visual representation of the overall trend in the data. It compares each data point to the line. The line is adjusted to be as close as possible to all the points at once.
Assume that a fair die is rolled. The sample space is (1, 2, 3, 4, 5, 6), and all the outcomes are equally likely. Find P(1) and express your answer in exact form.
1/6
If P(B^C)= 0.6, find P(B).
0.4
A fair coin is tossed three times. What is the probability that the sequence of tosses is HHH? Write your answer as a fraction or a decimal, rounded to four decimal places.
0.1250
Determine whether the association between the two variables is positive or negative.
The amount of time spent studying for a statistics exam and the score on the exam. Why?
Be specific!
Positive.
Large values of the amount of time spent studying for a statistics exam are associated with large values of the score on the exam.
Example: Spending 5 hours studying and getting a 95%, versus spending 20 minutes studying and getting a 60%.
Give the definition for Slope, Intercept, and Explanatory variable. Be specific, don't just list what they are represented by!
Slope (b): The amount by which y changes for each one unit increase in x.
Intercept (a): The value of y when x = 0.
Explanatory variable (x): X is the explanatory variable, explains "y-hat" (response variable) given what x equals.
Assume that a fair die is rolled. The sample space is (1, 2, 3, 4, 5, 6), and all the outcomes are equally likely. Find P(Less than six) and express your answer in exact form.
5/6
A baseball pitcher threw 3156 pitches. Of these, 1293 were thrown with no strikes on the batter, 908 were thrown with one strike, and 955 were thrown with two strikes. What is the probability that a baseball pitch is thrown with no strikes? Round your answer to four decimal places.
0.4097
A fair coin is tossed five times. What is the probability that all five tosses are tails? Write your answer as a fraction or a decimal, rounded to four decimal places.
0.0313
Compute the Correlation Coefficient. Round to three decimals. Explain!
11.1 Question #3
0.088
Compute the least-squares regression equation. Round the slope and y-intercept to four decimals.
11.2 Question #3.
y=5.306+1.462x
In a survey of 500 likely voters in a certain city, 285 said that they planned to vote to reelect the incumbent mayor.
What is the probability that a surveyed voter plans to vote to reelect the mayor?
0.57
A fair die is rolled seven times. What is the probability that it comes up 1 at least once? Write your answer as a fraction or a decimal, rounded to four decimal places.
0.7209
A fair die is rolled seven times. What is the probability that it comes up 1 at least once? Write your answer as a fraction or a decimal, rounded to four decimal places.
0.7209
Compute the Correlation Coefficient. Round to three decimals. Explain!
11.1 Question #4
-0.445
Complete the Linear regression equation. Predict about how far this person will travel after 10 hours of driving.
11.2 Question #4
617.51 miles
A student answered 800 multiple-choice questions during the semester. Of these, 320 were easy, 270 were medium, and 210 were hard. What is the probability that a randomly selected question was hard? Round to four decimal places.
0.2625
The following table presents the number of reports of graffiti in each of New York's five boroughs over a one-year period. These reports were classified as being open, closed, or pending. A graffiti report is selected at random. The report is open or comes from the Bronx. Round final answers to four decimal places.
4.2 Question #4
0.4252
Every day, Jorge buys a lottery ticket. Each ticket has a probability of 0.3 of winning a prize. After six days, what is the probability that Jorge has won at least one prize? Round your answer to four decimal places.
0.8824
Determine whether the correlation coefficient is an appropriate summary for the scatterplot and explain your reasoning.
11.1 Question #5
The correlation coefficient is not appropriate because there are outliers.
A car’s resale value is predicted using the Linear Regression Equation: y= 25,000 - 0.10x. Car A has 45,000 miles, and Car B has 30,000 miles. How much more is Car B expected to be worth than Car A?
1500
A survey asked 32,092 people how much confidence they had in educational institutions. Round your answers to four decimal places if necessary.What is the probability that a sampled person has either some OR hardly any confidence in educational institutions?
4.1 Question #5.
0.6880
An unfair coin has a probability of 0.4 of landing heads. The coin is tossed four times. What is the probability that it lands heads at least once?
0.8704
The probability that a certain make of car will need repairs in the first six months is 0.2. A dealer sells three such cars. What is the probability that at least one of them will require repairs in the first six months? Round your final answer to four decimal places.
0.4880