Introduction to Statistics Unit 4 Milestone 4 Exam
Data for price and thickness of soap is entered into a statistics software package and results in a regression equation of ŷ = 0.4 + 0.2x.
What is the correct interpretation of the slope if the price is the response variable and the thickness is an explanatory variable?
The price of the soap increases by $0.20, on average, when the thickness increases by 1 cm.
The price of the soap decreases by $0.40, on average, when the thickness increases by 1 cm.
The price of the soap increases by $0.40, on average, when the thickness increases by 1 cm.
The price of the soap decreases by $0.20, on average, when the thickness increases by 1 cm.
Peter analyzed a set of data with explanatory and response variables x and y.
He concluded the mean and standard deviation for x as 7.8 and 3.70, respectively.
He also concluded the mean and standard deviation for y as 12.2 and 4.15, respectively.
The correlation was found to be 0.964.
Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place.
Which of the following is a guideline for establishing causality?
Look for cases where correlation does not exist between the variables.
Do not consider other possible causes.
The experiment performed should be controlled and randomized.
Check if the effect is present or absent when the response variable is present or absent.
A correlation coefficient between average temperature and ice cream sales is most likely to be __________.
between 0 and –1
between –1 and –2
between 1 and 2
between 0 and 1
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Shawna finds a study of American men that has an equation to predict weight (in pounds) from height (in inches): ŷ = -210 + 5.6x. Shawna's dad’s height is 72 inches and he weighs 182 pounds.
What is the residual of weight and height for Shawna's dad?
11.2 pounds
809.2 pounds
193.2 pounds
-11.2 pounds
How many policies were sold when it snowed 2 to 4 inches?
The table below shows the grade and reading level for 5 students. For grade, the mean is 3.6 and the standard deviation is 2.1. For reading level, the mean is 9.2 and the standard deviation is 4.1. Using the formula below or Excel, find the correlation coefficient, r, for this set of students. Answer choices are rounded to the nearest hundredth.
0.92
1.00
0.85
0.71
The scatterplot below charts the performance of an electric motor.The scatterplot below charts the performance of an electric motor.
Explanatory variable: Voltage
Response variable: Rotation
Explanatory variable: Rotation
Response variable: Electric motor
Explanatory variable: Rotation
Response variable: Voltage
Explanatory variable: Voltage
Response variable: Electric motor
For this scatterplot, the r2 value was calculated to be 0.9382.Which of the following set of statements is true? There is no strong correlation in the linear association between beach visitors and daily temperatures. The correlation coefficient, r, is 0.880 About 94% of the variation in beach visitors is explained by a negative linear relationship with daily temperatures. The correlation coefficient, r, is 0.969. About 94% of the variation in beach visitors can be explained by a positive linear relationship with daily temperature. The correlation coefficient, r, is 0.969. About 94% of the variation in daily temperature can be explained by a positive linear relationship with beach visitors. The correlation coefficient, r, is 0.880
Which of the following scatterplots shows a correlation affected by non-linearity?
Brad reads a scatterplot that displays the relationship between the number of cars owned per household and the average number of citizens who have health insurance in neighborhoods across the country. The plot shows a strong positive correlation.
Brad recalls that correlation does not imply causation. In this example, Brad sees that increasing the number of cars per household would not cause members of his community to purchase health insurance.
Identify the lurking variable that is causing an increase in both the number of cars owned and the average number of citizens with health insurance.
The number of different car brands
Average annual salary per household
The number of citizens in the United States who do not have health insurance
Average health insurance costs in the United States
Thomas was interested in learning more about the salary of a teacher. He believed as a teacher increases in age, the annual earnings also increases. The age (in years) is plotted against the earnings (in dollars) as shown below.Using the best-fit line, approximately how much money would a 45-year-old teacher make?
$55,000
$58,000
$50,000
$48,000
Jesse takes two data points from the weight and feed cost data set to calculate a slope, or average rate of change. A ferret weighs 2.1 pounds and costs $3.40 per week to feed, while a Labrador Retriever weighs 70 pounds and costs $7.50 per week to feed.
Using weight as the explanatory variable, what is the slope of the line between these two points? Answer choices are rounded to the nearest hundredth.
$.06 / lb.
$16.56 / lb.
$1.62 / lb.
$1.73 / lb.
This scatterplot shows the performance of an electric motor using the variables speed of rotation and voltage. Select the answer choice that accurately describes the data's form, direction, and strength in the scatterplot.
Form: The data points are arranged in a curved line.
Direction: The speed of rotation increases with an increase in voltage.
Strength: The data points are far apart from each other.
Form: The data points are arranged in a curved line.
Direction: The voltage increases as the speed of rotation increases.
Strength: The data points are far apart from each other.
Form: The data points appear to be in a straight line.
Direction: The speed of rotation increases with an increase in voltage.
Strength: The data points are closely concentrated.
Form: The data points appear to be in a straight line.
Direction: The voltage increases as the speed of rotation increases.
Strength: The data points are closely concentrated.
This scatterplot shows the number of hours a student slept every night and his or her grade point average. The equation for the least-squares regression line to this data is: ŷ = 0.375x + 1.33. What is the predicted GPA for a student who sleeps 2.5 hours per day? Answer choices are rounded to the hundredths place.
2.08
2.27
2.46
2.64
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