5.9.1: Exercises

 

The table shows the GPA of 15 randomly selected students and the number of hours spent on studying their lessons before an exam. Use this information for problems 1 - 4.

Student	Number of Hours	GPA
1	3	2.5
2	3	2.4
3	6	3.5
4	4	3
5	5	3.2
6	6	3.8
7	3	2.7
8	4	2.6
9	2	2.8
10	5	3.4
11	5	3
12	4	3.3
13	5	3
14	4	2.7
15	8	4

1. Draw a scatter plot of the data.  Label the axes.
2. Based on the information provided, which best describes the relationship between students’ GPA and study habits? 
   1. Negative
   2. Positive
   3. No correlation
3. Based on the scatter plot, which statement accurately describes the information provided?
   1. The correlation is positive. As the number of hours spent on studying increases, the students’ GPA tends to increase.
   2. The correlation is negative. As the number of hours spent on studying increases, the students’ GPA tends to increase.
   3. The correlation is negative. As the number of hours spent on studying decreases, the students’ GPA tends to increase.
   4. The data show no relationship between students’ GPA and study habits.
4. Do the data imply that the length of time spent on studying before an exam causes the change in students’ GPA? Why or why not?
   1. Yes. Since hours spent on studying and GPA are correlated, it means the time spent on studying causes the GPA to increase.
   2. No. The increase in GPA could be attributed to other factors such as gender, class size, socioeconomic status, faculty qualification, and many others.
   3. No. The two variables are not correlated. Hence, the increase in time spent on studying does not affect the GPA.
   4. Yes. There is sufficient evidence to support the effect of study habits on  students’ GPA.
5. If there is a strong correlation between marijuana use and use of other drugs, can we conclude that using marijuana leads to using other drugs?
6. Describe whether the scatter plot of the following variables will show a positive correlation, a negative correlation, or no correlation.
   1. Height and weight
   2. Height and grade in a course
   3. Grade in a course and shoe size
   4. Hours of television watched and grade in a course
   5. Height and shoe size
   6. Hours of television watched and w eight
7. The table below shows the number of students in a class and the absences in a week.

   Class Size	15	18	20	20	25	25	30	35	35	40
   Number of Absences	5	2	10	4	8	12	2	5	7	10

   1. Draw a scatter plot and determine the relationship that best describes the data.
   2. Is the correlation between class size and the number of absences positive, negative, or zero?  Fill in the blank:  As the class size increases, the number of absences __________________.
8. The table below shows the recorded maximum average monthly temperature readings of a certain state in the US and the shipment of residential storage water heaters.

   \(\begin{array}{|l|l|l|}
   \hline \text { Month} & \text {Avg. Monthly Temperature } ^{\circ}\text{C}& \text{Shipment of water heaters (in units)} \\
   \hline \text { Jan}&-1 \;^\circ \text{C}&384,213  \\
   \hline \text { Feb}&\;\;0 \;^\circ \text{C}&745,570  \\
   \hline \text { Mar}&\;\;9 \;^\circ \text{C}&1,162,074   \\
   \hline \text { Apr}& \;15 \;^\circ \text{C}&1,473,757 \\
   \hline \text { May}& \;22 \;^\circ \text{C}&1,806,054   \\
   \hline \text { June}&\;27 \;^\circ \text{C}&2,217,780 \\
   \hline \text { July}&\;30 \;^\circ \text{C}&2,610,644  \\
   \hline \text { Aug}&\; 26  \;^\circ \text{C}&3,011,506   \\
   \hline \text { Sep} &\;24 \;^\circ \text{C}&3,377,667   \\
   \hline \text { Oct} &\;16 \;^\circ \text{C}&3,803,921   \\
   \hline\text { Nov} &\;12 \;^\circ \text{C}&4,162,667  \\
   \hline \text { Dec} &\;\;5 \;^\circ \text{C}&4,584,367  \\
   \hline
   \end{array}\)

   1. Draw a scatterplot.
   2. Describe the correlation that best describes the data provided.
9. In order to determine whether or not there is a relationship between the temperature and the chirp rate of a certain variety of cricket, the following data were collected.  Let x = ˚C and y = # chirps per second.

   \(\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}
   \hline x & 31.4 & 22.0 & 34.1 & 29.1 & 27.0 & 24.0 & 20.9 & 27.8 & 20.8 & 28.5 & 26.4 & 28.1 & 27.9 & 28.6 & 24.5 \\
   \hline y & 20.0 & 16.0 & 19.8 & 18.4 & 17.1 & 15.5 & 14.7 & 17.1 & 15.4 & 16.2 & 15.0 & 17.2 & 16.0 & 17.0 & 14.4 \\
   \hline
   \end{array}\)

   1. Draw a scatterplot of the data given.
   2. Is the correlation between temperature and chirp rate positive, negative, or zero?
   3. If the correlation is strong, can we conclude that temperature affects the chirp rate?
10. During the spring and summer, an ice cream shop kept track of the average daily temperature (in ˚F) and the amount of ice cream sales (in dollars).

    \(\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|}
    \hline \text { Temperature (} ^{\circ} {\text F)}  & 52 & 55 & 61 & 66 & 72 & 75 & 77 & 84 & 90 & 94 & 97 \\
    \hline \text{ Ice Cream Sales (\$)} & 3500 & 4200 & 5000 & 5300 & 6600 & 6800 & 7200 & 8000 & 8400 & 9100 & 9500 \\
    \hline
    \end{array}\)

    1. Create a scatterplot with this data.
    2. Use your scatterplot to make a prediction for the ice cream sales when the temperature is 70˚F.
    3. If ice cream sales were $7500, what do you think the average temperature was that day?