Question

(06.07)

A company is deciding whether or not to hire a new worker. The company must pay the worker hourly and cover a daily cost for insurance. The cost to pay an hourly worker for one day is represented by the function y = 8x + 25, where x is hours.

What is the y-intercept, and what does it represent? (1 point)


8; it represents the hourly wage for the worker
8; it represents the cost for insurance
25; it represents the cost for insurance
25; it represents the hourly wage for the worker
2. (06.07)
The price of a community pool membership has a one-time sign-up fee and a monthly fee. The price can be modeled by the function y = 20x + 50, where x is the number of months.

What is the slope, and what does it represent? (1 point)


20; it represents the monthly fee
20; it represents the one-time sign-up fee
50; it represents the monthly fee
50; it represents the one-time sign-up fee
3. (06.07)
How could the relationship of the data be classified? (1 point)

scatter plot with points loosely scattered going down to the right

A positive correlation
A causation
A negative correlation
No correlation
4. (06.07)
Given the data set for the length of time a person has been jogging and the person's speed, hypothesize a relationship between the variables. (1 point)


I would expect the data to be positively correlated.
I would expect the data to be negatively correlated.
I would expect no correlation.
There is not enough information to determine correlation.
5. (06.07)
You suspect that the spiciness of food served in a restaurant is positively correlated with number of soft drinks ordered. You have gathered several observations of people ordering food of different spice-levels and the number of soft drinks they ordered. What would be your next steps to test your hypothesis? (2 points)



Plot all data together on a dot plot to assess if there is any visible correlation between the data sets.
Offer a conclusion based on the data you observed.
Pick two points on the dot plot and find a line of best fit.
Find the correlation coefficient to see how well the line of best fit actually fits the data.
6. (06.07)
The correlation coefficient for practicing violin and getting better grades in a group of people is 0.8. Analyze the following statement:

Playing violin causes students to get better grades.

Is this a reasonable conclusion? (2 points)



Yes; students who play violin must necessarily get better grades
Yes; the correlation coefficient is above 0.5, so that implies causation
No; playing violin and earning better grades are completely unrelated
No; even though there is a strong positive correlation, playing violin doesn't cause students to get better grades
7. (06.07)
Analyze the following statement:

Brandon puts his water in the refrigerator so it will stay cold.

Is the statement an example of correlation or causation? (2 points)



Correlation, because there aren't enough observable trials
Causation, because a refrigerator keeps things cold
No relationship, because water temperature is independent of whether or not it is in a refrigerator

Answer 1

All the ones he answered above are Correct.

Answer 2

1. The equation of a line is y = mx + b, where m is the slope and b is the y-intercept. Therefore, the y-intercept is 25, and it represents the cost for insurance
2. The slope is m = 20, and it represents the monthly fee. (50 is the y-intercept.)
3. If the scatter plot's points loosely scattered going down to the right, this is a negative slope, and thus it is a negative correlation.
4. We would expect the data to be negatively correlated, since the longer a person has been jogging, the more tired he would be.
5. Plot all data together on a dot plot to assess if there is any visible correlation between the data sets. (The second step would be finding the correlation coefficient. Sometimes, a visual look already tells you whether or not there is a correlation. When uncertain, that's when the correlation coefficient must be calculated).
6. No; even though there is a strong positive correlation, playing violin doesn't cause students to get better grades. It may be that students who already have good grades decide to learn something new, so the learn to play the violin.
7. This is a causation, because a refrigerator keeps things cold. It is not just a correlation, but there is theoretical reason to expect the result.