Exam 3: Scatterplots and Correlation

Five strains of the Staphylococcus aureus bacteria were grown for 24 hours either at 35 degrees Celsius or at 43 degrees Celsius. Here are the resulting bacterial counts for each condition: 24 hours at 35 degrees Celsius 66 71 93 102 62 24 hours at 43 degrees Celsius 98 67 42 31 77 What is the approximate value of the correlation between bacterial count at 35 degrees Celsius and bacterial count at 43 degrees Celsius?

Do creative people make better teachers? Ten teachers at a large university were given a creativity test (scores range from 0 to 20, with higher scores indicating greater creativity) and were evaluated regarding teaching performance by students and peers (a score of 100 indicates an average performance, and larger scores indicate better performance). The creativity scores and teaching performance scores are given below. ? ? Creativity score Performance score 9 93 7 89 8 95 13 101 10 102 10 96 9 95 18 111 10 103 14 107 Use technology to obtain the correlation between creativity scores and teaching performance scores. Rounded to 3 decimal places, what is the correlation coefficient?

The data in the following scatterplot are from a small data set: The data were classified as being collected either in the winter or in the summer. Those collected in the winter are indicated by open circles, and those in the summer by solid circles. What can we say about the overall correlation of the data in this scatterplot?

The protease activity found in walnuts preserved in buffers of various pHs is listed in the following table: ? ? pH 4.5 5 6 7 8 9 10 protease activity 0.17 0.245 0.28 0.055 0.02 0 0.025 What can we conclude about the relationship between walnut protease activity and pH?

Tail-feather length in birds is sometimes a sexually dimorphic trait. That is, the trait differs substantially for males and for females. Researchers studied the relationship between weight (x) and tail-feather length (y) in a sample of five wild male long-tailed finches. Here are the data: What are the units of the correlation coefficient for these data? weight () tail length () 20.8 82.5 19.1 82.5 15.9 67.0 16.7 70.5 15.7 73.5

Five strains of the Staphylococcus aureus bacteria were grown at 35 degrees Celsius for either 24 hours or 48 hours. Here are the resulting bacterial counts for each condition: 24 hours at 35 degrees Celsius 66 71 93 102 62 48 hours at 35 degrees Celsius 110 123 146 136 113 Which of the following scatterplots is a correct representation of these data?

Consider the following scatterplot of the infected area of a plant versus the time since a pesticide was applied: What is the approximate value of the correlation between infected area and time since application?

A researcher states that the survival time of an organism is negatively related to the amount of a specific pollutant present in the ecosystem. What does this statement mean?

Do creative people make better teachers? Ten teachers at a large university were given a creativity test (scores range from 0 to 20, with higher scores indicating greater creativity) and were evaluated regarding teaching performance by students and peers (a score of 100 indicates an average performance, and larger scores indicate better performance). The creativity scores and teaching performance scores are given below. ? ? Creativity score Performance score 9 93 7 89 8 95 13 101 10 102 10 96 9 95 18 111 10 103 14 107 Which of the following scatterplots would appropriately display these data given the research question?

Tail-feather length in birds is sometimes a sexually dimorphic trait. That is, the trait differs substantially for males and for females. Researchers studied the relationship between weight (x) and tail-feather length (y) in a sample of five wild male long-tailed finches. Here are the data: Suppose the measurements were switched so that tail length was treated as an explanatory variable rather than a response variable. How would this switch affect the correlation? weight () tail length () 20.8 82.5 19.1 82.5 15.9 67.0 16.7 70.5 15.7 73.5

Do creative people make better teachers? Ten teachers at a large university were given a creativity test (scores range from 0 to 20, with higher scores indicating greater creativity) and were evaluated regarding teaching performance by students and peers (a score of 100 indicates an average performance, and larger scores indicate better performance). The creativity scores and teaching performance scores are given below. ? ? Creativity score Performance score 9 93 7 89 8 95 13 101 10 102 10 96 9 95 18 111 10 103 14 107 If we were to accidentally switch the explanatory and response variables, how would this switch affect the correlation coefficient?

Bird species from temperate regions must cope with relatively short breeding seasons. A study examined the relationship between blood testosterone level (ng/ml) and the duration of the egg-laying period (months) in temperate bird species. The following scatterplot displays this relationship, after taking the logarithm of each variable: Which units should be attached to the correlation r?

Does atmospheric pressure have an impact on plant heights? To study this question, 20 Spartina alterniflora plants were planted at sea level (1 atmosphere), while another 20 Spartina alterniflora plants were grown in a special chamber aboard the International Space Station (ISS) (0 atmospheres). The height of the plants after 3 months was recorded. The goal was to see whether the plant heights (in centimeters) were affected by the atmospheric pressure exerted on the plant. What is the response variable in this study?

A research study of approximately 13,900 incoming freshmen in U.S. universities and colleges looked at the relationship between the amount of time a student spends drinking alcohol and the student's GPA, with a negative association observed between the two variables. What is the explanatory variable in this study?

Tail-feather length in birds is sometimes a sexually dimorphic trait. That is, the trait differs substantially for males and for females. Researchers studied the relationship between weight (x) and tail-feather length (y) in a sample of five wild male long-tailed finches. Here are the data: Based on these data, what can we conclude? weight () tail length () 20.8 82.5 19.1 82.5 15.9 67.0 16.7 70.5 15.7 73.5

When water flows across farm land, some of the soil is washed away, resulting in erosion. An experiment was conducted to investigate the effect of the rate of water flow (in liters per second) on the amount of soil washed away (in kilograms). The data are given in the following table: ? ? Flow rate 0.31 0.85 1.26 2.47 3.75 Eroded soil 0.82 1.95 2.18 3.01 6.07 What is the best description of the association between flow rate and amount of eroded soil?

Five strains of the Staphylococcus aureus bacteria were grown for 24 hours either at 35 degrees Celsius or at 43 degrees Celsius. Here are the resulting bacterial counts for each condition: 24 hours at 35 degrees Celsius 66 71 93 102 62 24 hours at 43 degrees Celsius 98 67 42 31 77 Which of the following scatterplots is a correct representation of these data?

The following scatterplot shows heights (in centimeters) of Spartina alterniflora plants against the amount of sunlight they were given (in minutes). Those plants grown at sea level are represented by a closed circle and those grown on the International Space Station (ISS) (0 atmospheres) are shown with an open circle. What can we conclude from this scatterplot?

Five strains of the Staphylococcus aureus bacteria were grown for 24 hours either at 35 degrees Celsius or at 43 degrees Celsius. Here are the resulting bacterial counts for each condition: 24 hours at 35 degrees Celsius 66 71 93 102 62 24 hours at 43 degrees Celsius 98 67 42 31 77 Suppose we had plotted bacterial count at 35 degrees Celsius on the y axis instead of the x axis. How would this change affect the value of the correlation coefficient?

Tail-feather length in birds is sometimes a sexually dimorphic trait. That is, the trait differs substantially for males and for females. Researchers studied the relationship between weight (x) and tail-feather length (y) in a sample of five wild male long-tailed finches. Here are the data: weight () tail length () 20.8 82.5 19.1 82.5 15.9 67.0 16.7 70.5 15.7 73.5 Which of the following scatterplots is a correct representation of these data?