1. The following data table is obtained by a fourth grader on his science project, "Exploding Foam." He poured 1/2 tea-spoon of baking soda and 1/8 tea-spoon of laundry detergent into 1/4 cup (50ml) of vinegar of various temperature, and measured the volume of the foam. Num. Temp. Vol. Num. Temp. Vol. Num. Temp. Vol. 1 45.5°F 250ml 41.4°F 175ml 43.0°F 300ml 44.6°F 350ml 52.0°F 300ml 6. 71.9°F 400ml 48.5°F 250ml 96.6°F 550ml 7 44.1°F 500ml 8 52.4°F 300ml 9. 10 57.9°F 300ml 11 75.1°F 450ml 12 13 123.6°F 600ml 14 120.1°F 600ml 15 104.6°F 550ml 16 89.3°F 500ml 17 101.1°F 400ml 18 94.4°F 550ml 19 94.3°F 550ml Mean SD Cor (a) Find the means (i and g). (b) Find the standard deviations (s, and s,). (c) Find the correlation coefficient (r).
1. The following data table is obtained by a fourth grader on his science project, "Exploding Foam." He poured 1/2 tea-spoon of baking soda and 1/8 tea-spoon of laundry detergent into 1/4 cup (50ml) of vinegar of various temperature, and measured the volume of the foam. Num. Temp. Vol. Num. Temp. Vol. Num. Temp. Vol. 1 45.5°F 250ml 41.4°F 175ml 43.0°F 300ml 44.6°F 350ml 52.0°F 300ml 6. 71.9°F 400ml 48.5°F 250ml 96.6°F 550ml 7 44.1°F 500ml 8 52.4°F 300ml 9. 10 57.9°F 300ml 11 75.1°F 450ml 12 13 123.6°F 600ml 14 120.1°F 600ml 15 104.6°F 550ml 16 89.3°F 500ml 17 101.1°F 400ml 18 94.4°F 550ml 19 94.3°F 550ml Mean SD Cor (a) Find the means (i and g). (b) Find the standard deviations (s, and s,). (c) Find the correlation coefficient (r).
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Transcribed Image Text:Math 1680 Elementary Probability and Statistics
Exercise Set 3
Name:
1. The following data table is obtained by a fourth grader on his science project, "Exploding
Foam." He poured 1/2 tea-spoon of baking soda and 1/8 tea-spoon of laundry detergent into
1/4 cup (50ml) of vinegar of various temperature, and measured the volume of the foam.
Num. Temp.
1 45.5°F 250ml
44.6°F 350ml
Vol. Num. Temp.
Vol. Num. Temp.
Vol.
3 43.0°F 300ml
2 41.4°F 175ml
52.0°F 300ml
52.4°F 300ml
75.1°F 450ml
14 120.1°F 600ml
4
71.9°F 400ml
44.1°F 500ml
57.9°F 300ml
13 123.6°F 600ml
89.3°F 500ml
94.3°F 550ml
48.5°F 250ml
96.6°F 550ml
15 104.6°F 550ml
7
8
10
11
12
16
17 101.1°F 400ml
18
94.4°F 550ml
19
Mean
SD
Cor
(a) Find the means (7 and g).
(b) Find the standard deviations (s, and s,).
(c) Find the correlation coefficient (r).
(d) Produce a scatter plot.
2. Based on the data set of Problem 1, find the best point-estimate of the volume of the foam,
when the temperature of the vinegar is 65°F. For an extra credit, back up your computation
visually, by presenting the scatter plot and the regression line.
3. Based on the data set of Problem 1, find the best point-estimate of the temperature of the
vinegar, if the volume of the foam is 380ml. For an extra credit, justify your computation
visually, by presenting the scatter plot and the regression line.
Expert Solution
Step 1
Let X be the temperature in o F and
Y be the volume ml
n = number of observations = 19
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