Exam 11: Two Quantitative Variables

The following scatterplot displays the finish time (in minutes) and age (in years) for the male racers at the 2018 Strawberry Stampede (a 10k race through Arroyo Grande). -Approximate the value of the correlation coefficient for these data.

Babies born with low birth weights (less than 2500 grams) are at an increased risk for many infant diseases. Researchers in North Carolina collected data to see what variables may influence the birth weight (in grams) of a child, including whether the mother drank alcohol during pregnancy, whether the mother smoked during pregnancy, the mother's age (years), the gestation of the pregnancy (number of weeks from conception until birth), the mother's race, the length of the birth (hours), and several others. The plot below summarizes some of the variables measured. -Based on the plot, does there appear to be an association between gestation period and birth weight?

Social warmth is a term referring to the feeling of being connected to others. A study published in PLoS One in 2016 looked at a potential relationship between physical warmth (body temperature) and social warmth among a group of 54 volunteers (Inagki et al.). These volunteers had their oral temperature taken by a registered nurse and then assessed themselves using a scale of 1 to 5 on twelve items related to a feeling of social connection for which the average was recorded. Higher average scores indicated higher levels of social warmth. The theory was that the thermoregulatory system, which helps maintain a relatively warm internal body temperature, may also help people assess feelings of social connection. Below is a scatterplot and least-squares regression line of the data. -Which of the following is the correlation coefficient for these data?

Babies born with low birth weights (less than 2500 grams) are at an increased risk for many infant diseases. Researchers in North Carolina collected data to see what variables may influence the birth weight (in grams) of a child, including whether the mother drank alcohol during pregnancy, whether the mother smoked during pregnancy, the mother's age (years), the gestation of the pregnancy (number of weeks from conception until birth), the mother's race, the length of the birth (hours), and several others. The plot below summarizes some of the variables measured. -What type of plot would be appropriate for examining the relationship between a mother's age and her baby's birth weight?

The following scatterplot displays the finish time (in minutes) and age (in years) for the male racers at the 2018 Strawberry Stampede (a 10k race through Arroyo Grande). -If 70-year-old male with a finishing time of 35 minutes was added to the data set, would the correlation coefficient increase, decrease, or remain the same?

Babies born with low birth weights (less than 2500 grams) are at an increased risk for many infant diseases. Researchers in North Carolina collected data to see what variables may influence the birth weight (in grams) of a child, including whether the mother drank alcohol during pregnancy, whether the mother smoked during pregnancy, the mother's age (years), the gestation of the pregnancy (number of weeks from conception until birth), the mother's race, the length of the birth (hours), and several others. The plot below summarizes some of the variables measured. -For each of the three variables displayed in the plot, state whether they are categorical or quantitative. Weight: Gestation: Smoke:

Are people with bigger brains more intelligent? Forty college students volunteered to participate in a study which examined brain size (measured as 1000's of pixels counted in a brain scan), and IQ scores (measured in points). A scatterplot of the data is shown below. -State the null and alternative hypotheses using proper notation.

Data from gapminder.org on 184 countries was used to examine if there is an association between (average) female life expectancy (that is, the average lifespan of women in the country) and the average number of children women give birth to for the year 2019. A scatterplot of the data follows. -What are the observational units?

How is the number of pages in a textbook related to the price of the textbook? To find out, two Cal Poly freshmen (2006) randomly selected 30 textbooks at the campus bookstore and recorded the price ($) and number of pages for each book. Here's output from analyzing the data collected in the Corr/Regression applet. Assume, for now, that the normal approximation-based method is valid, and thus, the p-value from the Regression Table below is valid. -We can conclude that the price of a textbook will increase if we add more pages.

Estimate the value of the correlation coefficient between the two variables shown in the following scatterplot.

It is commonly expected that as a person ages, their muscle mass decreases. To further examine this relationship in women, a nutritionist randomly selected 60 female patients from her clinic, 15 women from each 10-year age group beginning with age 40 and ending with age 80. For each patient, her age and current muscle mass was recorded. A scatterplot, least squares regression line, and coefficient of determination are as follows. -What is the value of the correlation coefficient between age and muscle mass for these data?

Data from gapminder.org on 184 countries was used to examine if there is an association between (average) female life expectancy (that is, the average lifespan of women in the country) and the average number of children women give birth to for the year 2019. A scatterplot of the data follows. -The p-value for this test is less than 0.001. What can we conclude?

How is the number of pages in a textbook related to the price of the textbook? To find out, two Cal Poly freshmen (2006) randomly selected 30 textbooks at the campus bookstore and recorded the price ($) and number of pages for each book. Here's output from analyzing the data collected in the Corr/Regression applet. Assume, for now, that the normal approximation-based method is valid, and thus, the p-value from the Regression Table below is valid. -What is the most appropriate null hypothesis for testing the regression slope using theory-based methods?