Bivariate Data Worksheets Grade 11

1. A researcher is studying the relationship between study hours and test scores. The regression equation is ŷ = 2.5x + 65, where x represents study hours and ŷ represents predicted test score. The correlation coefficient is r = 0.85. If a student studies for 6 hours, what is their predicted test score according to this model?
2. A marine biologist is studying the relationship between water temperature (°C) and coral growth rate (mm/year) across 25 reef sites. She calculates a linear regression equation of ŷ = 12.5 - 0.4x, where x represents water temperature and ŷ represents predicted coral growth rate. The standard error of the slope is 0.08. Test the hypothesis that water temperature affects coral growth at the α = 0.01 significance level by calculating the t-statistic for the slope coefficient.
3. Isabella, a high school science teacher, surveyed 112 Grade 11 students to investigate the relationship between whether a student plays a musical instrument and whether they participate in a school sports team. She recorded the data in a two-way table. Of the 48 students who play a musical instrument, 28 also play a sport. Of the 64 students who do not play a musical instrument, 48 play a sport. Construct a two-way table to represent this bivariate categorical data distribution, then calculate the percentage of students who play a musical instrument but do not play a sport, rounded to the nearest whole percent.

…and 3 more problems

1. Mason surveyed 32 students at his school about their preferred study method (visual or textual) and their performance on a recent math test. He recorded the following data: 12 students preferred visual learning and scored above 82%, while 7 students preferred visual learning and scored 82% or below. Among those who preferred textual learning, 8 scored above 82% and 5 scored 82% or below. Construct a two-way frequency table for this bivariate categorical data. Then, calculate the conditional relative frequency of scoring above 82% among students who prefer visual learning, and interpret its meaning in context.
2. Create a scatter plot for Hana's data: (2,8), (4,12), (6,16), (8,20), (10,24), (12,28), (14,32), (16,36), (18,40), (20,44). Identify the correlation type and calculate the slope of the line of best fit.
3. Create a scatter plot for Tane's data: (5,13), (9,21), (13,29), (17,37), (21,45), (25,53), (29,61), (33,69), (37,77), (41,85). Calculate the correlation coefficient r.

…and 2 more problems

1. Emma is studying the relationship between the number of hours of sunlight per day (x) and the height (in cm) of sunflower plants (y) after 30 days. She collects data from 11 plants and records the following ordered pairs: (5, 13), (7, 17), (9, 21), (11, 25), (13, 29), (15, 33), (17, 37), (19, 41), (21, 45), (23, 49), (25, 53). Create a scatter plot of this bivariate data, describe the form, direction, and strength of the distribution, and determine the linear regression equation that models the relationship.
2. A medical researcher is studying the relationship between daily exercise time (in minutes) and resting heart rate (in beats per minute) for adults. After collecting data from 50 participants, the researcher calculates a linear regression equation of ŷ = 72 - 0.15x, where x represents daily exercise time and ŷ represents predicted resting heart rate. The correlation coefficient is -0.68. If a new participant exercises for 40 minutes daily, what would be their predicted resting heart rate according to this model?
3. Noah, a city planner, surveyed 81 residents in two neighborhoods, Eastside and Westside, about their preferred mode of transportation for commuting to work: car, bus, or bicycle. The results showed that in Eastside, 16 residents preferred cars, 11 preferred buses, and 6 preferred bicycles. In Westside, 21 residents preferred cars, 16 preferred buses, and 11 preferred bicycles. Construct a two-way table to represent this bivariate data with neighborhood and transportation preference as the two categorical variables. Then, calculate the conditional relative frequency of residents who prefer bicycles given that they live in Westside, expressed as a percentage rounded to the nearest whole number.

…and 2 more problems