1. Find the mass of each of these objects on the earth.
1 answer:
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Fun. I prefer Oxymetazoline.
For the control group we have a headache probability of
c = 368/1671 = .220
For the experimental group we have a headache probability of
e = 494/2013 = .245
The observed difference is
d = e - c = .025
The variance of the difference is
s² = c(1-c)/n₁ + e(1-e)/n₂
so the standard deviation is
We get a t statistic on the difference of
t = d/s = .025/.0139 = 1.79
We're interested in the one sided test, P(d > 0). We have enough dfs to assume normality. We look up in the standard normal table
P(z < 1.79) = .96327
so
p = P(z > 1.79) = 1 - .96327 = 0.037 = 3.7%
Answer: That's less that 10% so we have evidence to conclude that headaches are significantly greater in the experimental group.
Given:
x: [1 2 3 4 5 6 7]
y: [9 9.5 10.25 11.25 12.5 14 15.75]
Let the function which models the data be
y(x) = ax² + bx + c
Apply the function to the first three data points
a + b + c = 9 .(1)
4a + 2b + c = 9.5 (2)
9a + 3b + c = 10.25 (3)
Subtract (1) from (2).
3a + b = 0.5
or
b = 0.5 - 3a (4)
Subtract (1) from (3).
8a + 2b = 1.25 (5)
Substitute (4) into (5).
8a + 2(0.5 - 3a) = 1.25
2a = 0.25
a = 0.125
From (4),
b = 0.5-3*0.125 = 0.125
From (1),
c = 9 - 0.125 - 0.125 = 8.75
The function is
y = 8.75 + 0.125x + 0.125x²
Check that the function works for x=4,5,6,7.
From the calculator, obtain
y(4) = 11.25 Correct
y(5) = 12.5 Correct
y(6) = 14 Correct
y(7) = 15.75 Correct
The graph of the function is shown below.
Answer: y = 8.75 + 0.125x + 0.125x²
x: [1 2 3 4 5 6 7]
y: [9 9.5 10.25 11.25 12.5 14 15.75]
Let the function which models the data be
y(x) = ax² + bx + c
Apply the function to the first three data points
a + b + c = 9 .(1)
4a + 2b + c = 9.5 (2)
9a + 3b + c = 10.25 (3)
Subtract (1) from (2).
3a + b = 0.5
or
b = 0.5 - 3a (4)
Subtract (1) from (3).
8a + 2b = 1.25 (5)
Substitute (4) into (5).
8a + 2(0.5 - 3a) = 1.25
2a = 0.25
a = 0.125
From (4),
b = 0.5-3*0.125 = 0.125
From (1),
c = 9 - 0.125 - 0.125 = 8.75
The function is
y = 8.75 + 0.125x + 0.125x²
Check that the function works for x=4,5,6,7.
From the calculator, obtain
y(4) = 11.25 Correct
y(5) = 12.5 Correct
y(6) = 14 Correct
y(7) = 15.75 Correct
The graph of the function is shown below.
Answer: y = 8.75 + 0.125x + 0.125x²