Exam 10: Relationships Between Measurement Variables

Explain how sample size can affect whether or not a relationship is found to be statistically significant (discuss the very small and very large sample cases).

Explain the difference between a statistical relationship and a deterministic relationship.

The __________ between two measurement variables is an indicator of how closely their values fall to a straight line.

The __________ of the sample can greatly affect whether or not a relationship is found to be statistically __________.

What type of statistical error is being made in the following statement? "If this uphill linear trend continues, 50 years from now, one out of every three of us will be an Elvis impersonator."

If there is no linear relationship between two measurement variables, the correlation is __________.

For Questions , use the following narrative Narrative: Study time and exam score Suppose an algebra professor found that the correlation between study time (in hours) and exam score (out of 100) is +.80, and the regression line was found to be y = 20 + 4x.He arrived at this equation through years of collecting data on his students, most of whom reported studying anywhere from 0 to 20 hours for his exams. -{Study time and exam score narrative} For which values of study time does the professor's regression equation make sense in terms of predicting exam scores?

For Questions , use the following narrative Narrative: Study time and exam score Suppose an algebra professor found that the correlation between study time (in hours) and exam score (out of 100) is +.80, and the regression line was found to be y = 20 + 4x.He arrived at this equation through years of collecting data on his students, most of whom reported studying anywhere from 0 to 20 hours for his exams. -{Study time and exam score narrative} Suppose the professor later found out that his correlation was not +.80, but rather it was +.08.How does this change the predictions he can make about exam scores based on study time?

For Questions , use the following narrative Narrative: Study time and exam score Suppose an algebra professor found that the correlation between study time (in hours) and exam score (out of 100) is +.80, and the regression line was found to be y = 20 + 4x.He arrived at this equation through years of collecting data on his students, most of whom reported studying anywhere from 0 to 20 hours for his exams. -{Study time and exam score narrative} Which variable is X and which variable is Y in this situation?

For Questions , use the following narrative Narrative: Study time and exam score Suppose an algebra professor found that the correlation between study time (in hours) and exam score (out of 100) is +.80, and the regression line was found to be y = 20 + 4x.He arrived at this equation through years of collecting data on his students, most of whom reported studying anywhere from 0 to 20 hours for his exams. -{Study time and exam score narrative} What meaning (if any) does the y intercept of 20 have in this situation? Use words that a non-statistics student would be able to understand.

Most researchers are willing to declare that a relationship is statistically significant if the chances of observing the relationship in the sample when actually nothing is going in the population are less than what percent?

For Questions , use the following narrative Narrative: Crickets and temperature A researcher wants to explore the relationship between cricket chirps and temperature.The following scatterplot shows data collected over a random sample of 8 days.Each day, the temperature was recorded, as well as the number of times a cricket chirped in 15 seconds.The correlation was found to be over .90.The least squares line was found to be Temperature (in Fahrenheit) = 40 + 1.0 × (#Chirps in 15 seconds). -{Crickets and temperature narrative} On nights when crickets chirp 120 times per minute, what do you predict the temperature to be, on average?

A researcher wants to explore the relationship between cricket chirps and temperature.The following scatterplot shows data collected over a random sample of 8 days.Each day, the temperature was recorded, as well as the number of times a cricket chirped in 15 seconds.According to this scatterplot, what can be said (if anything) about the relationship between cricket chirps and temperature?

A relationship is considered to be statistically significant if that relationship is stronger than what percent of the relationships we would expect to see just by chance?

Explain how a relationship may exist between two variables in a sample even if there is no relationship between the two variables in that population.

Statistical relationships such as correlation are useful for describing features of __________.

For Questions , use the following narrative Narrative: Crickets and temperature A researcher wants to explore the relationship between cricket chirps and temperature.The following scatterplot shows data collected over a random sample of 8 days.Each day, the temperature was recorded, as well as the number of times a cricket chirped in 15 seconds.The correlation was found to be over .90.The least squares line was found to be Temperature (in Fahrenheit) = 40 + 1.0 × (#Chirps in 15 seconds). -{Crickets and temperature narrative} On nights when crickets chirp 20 times in 15 seconds, what do you predict the temperature to be, on average?

To be convincing, an observed relationship must also be statistically __________.

Determine whether or not the following statement could be statistically correct.If not, explain why not."We found a strong correlation between gender and political party."

Determine whether or not the following statement could be statistically correct.If not, explain why not."The correlation between height and weight is +0.8, so the correlation between weight and height must be −0.8."