# Correlations, Statistics Problem Example

Imagine that you are interested in whether there is a relationship between the amount of coffee people drink and the number of hours they sleep each night. Determine whether you expect a positive or a negative relationship between the cups of coffee people drink and the number of hours they sleep.

Based on intuitive logic, one would expect a negative relationship between the number of cups of coffee an individual drinks and the fewer number of hours they sleep.

Ask 12 friends or family members how many cups (approximately 8 oz.) of coffee they drink each day and how many hours they sleep each night. Create a table that includes each participant, a column for cups of coffee, and a column for sleep

Participant        Cups of Coffee (X)       Hours of Sleep (Y)

Erik                             4                                 7

Joe                              3                                 8

Ted                              1                                 6

Jose                             3                                 9

Victor                          3                                 5

Claire                          0                                 7

Suzanne                       2                                 9

Jorge                           4                                 8

Dan                             6                                 6

Jayeoon                       2                                 12

Hwangjin                     4                                 4

Erika                           2                                 9

Create a scatter diagram using Figure 10.1 as a guide. Draw a line through the scatter diagram.

Post the list of scores for your participants. Then respond briefly to each of the following questions about your findings:

What does your scatter diagram look like? Briefly describe it.

The data points are relatively concentrated together with a few vertical outliers.  The intercept was 8.265, and the coefficient for coffee was -.3976.

Based on your prediction about the relationship between the amount of coffee people drink and the number of hours they sleep, what is your H0 and what is your HA ?

My prediction is correct- they had a negative relationship as the coefficient for coffee is a negative.

Did you find a positive linear relationship or a negative linear relationship? How do you know?

Weak negative relationship- the correlation coefficient is -.30.

If you were pursuing this study, what calculations would you perform to describe this relationship and why?

Correlation coefficient- to understand correlation between variables

Bivariate Regression- it would help to understand what the average cup of coffee does to total sleeping time

Without completing the calculations, assume that you obtained a significant result. What would you conclude?

I would conclude that drinking coffee  is correlated with fewer hours of sleep.