Question

Doctors suspect a strain of bacteria found in the hospital is becoming resistant to antibiotics. They put various concentrations of antibiotic in petri dishes and add some of the bacteria to allow it to grow. The bacteria grow into groups in the dish called colonies. After some time, the doctors return to the petri dishes and count the number of colonies for the different amounts of antibiotic. The data is plotted with a best fit line. The correlation coefficient was r = -0.83 1) What does the sign of correlation coefficient (r=-0.83) tell you about the relationship between the number of bacteria colonies and the concentration of antibiotic in the dish? 2) What does the numerical value of the correlation coefficient (r=-0.83) tell you about the relationship between the number of bacteria colonies and the concentration of antibiotic in the dish?3) In a follow-up study, a group of scientists collect data that was fit by a linear model with a correlation coefficient of r=-0.94. Which study suggests a stronger relationship between the number of bacteria colonies and the concentration of antibiotic----the doctors' study or the scientists' study?

Answer 1

1) When the concentration of the antibiotic increase, the number of bacteria colonies decrease

2) There is a relationship between the concentration of the antibiotic and the number of bacterias colonies.

3) The scientists' study

Step-by-step explanation:

A correlation coefficient is a number between -1 and 1 that gives a measure of the relationship between the variables.

If the correlation coefficient is close to 1, there is a positive relationship between the variables, which means that when one variable increases the other also increases.

If the correlation coefficient is close to -1, there is a negative relationship between the variable, so if one variable increases the other decrease.

If the correlation coefficient is close to 0 there is no relationship between the variables.

Therefore, the sign of the correlation coefficient r = -0.83 tell us that when the concentration of the antibiotic increase, the number of bacteria colonies decrease. So, there is a negative relationship between the variables.

The numerical value -0.83 tell us that there is a relationship between the number of bacteria colonies and the concentration of antibiotic. So, the bacteria is not resistant to the antibiotics.

Finally, if the scientists' study has a correlation coefficient of r = -0.94 that is closer to -1 than the correlation coefficient of the doctor's study r = -0.83, then, the study that suggests a stronger relationship is the scientists' study.