Solution:
To test the hypothesis is that the mean ozone level is different from 4.40 parts per million at 1% of significance level.
The null hypothesis and the alternative hypothesis is :
![$H_0: \mu = 4.40$](https://tex.z-dn.net/?f=%24H_0%3A%20%5Cmu%20%3D%204.40%24)
![$H_a: \mu \neq 4.40$](https://tex.z-dn.net/?f=%24H_a%3A%20%5Cmu%20%5Cneq%204.40%24)
The z-test statistics is :
![$z=\frac{\overline x - \mu}{\left( \sigma / \sqrt n \right)} $](https://tex.z-dn.net/?f=%24z%3D%5Cfrac%7B%5Coverline%20x%20-%20%5Cmu%7D%7B%5Cleft%28%20%5Csigma%20%2F%20%5Csqrt%20n%20%5Cright%29%7D%20%24)
![$z=\frac{4.2 - 4.4}{\left(0.7 / \sqrt{23} \right)} $](https://tex.z-dn.net/?f=%24z%3D%5Cfrac%7B4.2%20-%204.4%7D%7B%5Cleft%280.7%20%2F%20%5Csqrt%7B23%7D%20%5Cright%29%7D%20%20%24)
![$z =\frac{-0.2}{0.145}$](https://tex.z-dn.net/?f=%24z%20%3D%5Cfrac%7B-0.2%7D%7B0.145%7D%24)
z = -1.37
The z critical value for the two tailed test at 99% confidence level is from the standard normal table, he z critical value for a two tailed at 99% confidence is 2.57
So the z critical value for a two tailed test at 99% confidence is ± 2.57
Conclusion :
The z values corresponding to the sample statistics falls in the critical region, so the null hypothesis is to be rejected at 1% level of significance. There is a sufficient evidence to indicate that the mean ozone level is different from 4.4 parts per million. The result is statistically significant.
Answer:
$2282
Step-by-step explanation:
ƒ(x) = x(4564-x) = 4564x - x²
In standard form,
ƒ(x) = -x² + 4564x
a = -1; b = 4564; c = 0
This is the equation of an inverted parabola, because a < 0. Therefore, the vertex is a maximum.
The vertex of a parabola occurs at
x = -b/(2a) = -4564/[-2 × (-1)] = -4564/(-2) = 2282.
The price that will maximize the company's revenue is $2282.
The graph below shows that the company's maximum revenue is over $5.2 million.
- Answer: D.
Step-by-step explanation:
Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula.
Answer:
\[v(t)=\underset{\text{Δ}t\to 0}{\text{lim}}\frac{x(t+\text{Δ}t)-x(t)}{\text{Δ}t}=\frac{dx(t)}{dt}.\]
Step-by-step explanation: