Using Lagrange multipliers, we have the Lagrangian

with partial derivatives (set equal to 0)




Substituting the first three equations into the fourth allows us to solve for

:

For each possible value of

, we get two corresponding critical points at

.
At these points, respectively, we get a maximum value of

and a minimum value of

.
X + 13 = -4
x = -4 - 13
x = - 17
I am thinking it is the first one..solution is -17
Answer:
380.
Just add the two numbers together and it'll work :)
Answer:
Note: The full question is attached as picture below
a) Hо : p = 0.71
Ha : p ≠ 0.71
<em>p </em>= x / n
<em>p </em>= 91/110
<em>p </em>= 0.83.
1 - Pо = 1 - 0.71 = 0.29.
b) Test statistic = z
= <em>p </em>- Pо / [√Pо * (1 - Pо ) / n]
= 0.83 - 0.71 / [√(0.71 * 0.29) / 110]
= 0.12 / 0.043265
= 2.77360453
Test statistic = 2.77
c) P-value
P(z > 2.77) = 2 * [1 - P(z < 2.77)] = 2 * 0.0028
P-value = 0.0056
∝ = 0.01
P-value < ∝
Reject the null hypothesis. There is sufficient evidence to support the researchers claim at the 1% significance level.