Solution :
Given :
![$\mu = 24$](https://tex.z-dn.net/?f=%24%5Cmu%20%3D%2024%24)
n = 15
![$\overline x = 24.89$](https://tex.z-dn.net/?f=%24%5Coverline%20x%20%3D%2024.89%24)
s = 0.5902
The hypothesis :
![$H_0 : \mu = 25$](https://tex.z-dn.net/?f=%24H_0%20%3A%20%5Cmu%20%3D%2025%24)
![$H_a : \mu \neq 25$](https://tex.z-dn.net/?f=%24H_a%20%3A%20%5Cmu%20%5Cneq%2025%24)
This is a 2 tailed test.
The significance level is ![$95 \% \ ( \alpha =0.05)$](https://tex.z-dn.net/?f=%2495%20%5C%25%20%5C%20%28%20%5Calpha%20%3D0.05%29%24)
The test statistic :
![$Z=\frac{\overline x - \mu}{\frac{\sigma}{\sqrt n}}$](https://tex.z-dn.net/?f=%24Z%3D%5Cfrac%7B%5Coverline%20x%20-%20%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%20n%7D%7D%24)
![$Z=\frac{24.89-25}{\frac{0.5902}{\sqrt 15}}$](https://tex.z-dn.net/?f=%24Z%3D%5Cfrac%7B24.89-25%7D%7B%5Cfrac%7B0.5902%7D%7B%5Csqrt%2015%7D%7D%24)
= -0.72
The p value : The p value for Z = -0.72 is 0.4716
The critical value : the critical value at α = 0.05 is +1.96 to -1.96
The decision rule :
If
or if
, then reject
.
Also if p value is less than α, then reject
.
The decision :
Since the Z falls in between +1.96 and -1.96, we fail to reject the
. Also since p value is greater than α, we fail to reject
.
The conclusion :
There is not sufficient evidence at the 95% significance level to warrant rejection of the claim that the pills come from a population in which the amount of the atorvastatin is equal to 25 mg.
Now calculating the mean and the standard deviation :
![$\text{Mean} = \frac{\text{sum of observation}}{\text{total observations}}$](https://tex.z-dn.net/?f=%24%5Ctext%7BMean%7D%20%3D%20%5Cfrac%7B%5Ctext%7Bsum%20of%20observation%7D%7D%7B%5Ctext%7Btotal%20observations%7D%7D%24)
Standard deviation = ![$\sqrt{\text{variance}}$](https://tex.z-dn.net/?f=%24%5Csqrt%7B%5Ctext%7Bvariance%7D%7D%24)
Variance = ![$\frac{\text{sum of squares(SS)}}{n-1}$](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Ctext%7Bsum%20of%20squares%28SS%29%7D%7D%7Bn-1%7D%24)
Where, SS = ![$\sum (X - \text{mean})^2$](https://tex.z-dn.net/?f=%24%5Csum%20%28X%20-%20%5Ctext%7Bmean%7D%29%5E2%24)
X Mean ![$(X-\text{mean})^2$](https://tex.z-dn.net/?f=%24%28X-%5Ctext%7Bmean%7D%29%5E2%24)
24.1 24.89 0.62
24.4 24.89 0.24
24.3 24.89 0.35
24.9 24.89 0
24.1 24.89 0.62
24.2 24.89 1.72
24.1 24.89 0.04
26.2 24.89 0.04
25.1 24.89 0.24
25 24.89 0.01
24.7 24.89 0.04
25.1 24.89 0.04
25.3 24.89 0.17
25.5 24.89 0.37
25.5 24.89 0.37
n 15
Sum 373.3
Average 24.89
SS 4.8775
Variance =
0.348392857
Standard deviation 0.5902
Answer:
8333 tickets.
Step-by-step explanation:
If you take 20,000 and divide it by 12 you get 1666.66
You then take 1666.66 and times it by 5.
The answer you get is 8333.33 but the instructions say to round it to the nearest whole number which would be 8333. Hope this helps!!
Mlachi is wrong 1/3 times -30 = 10 not 30
first, love the killua profile picture ! i love hunterxhunter i am currently on season 5, episode 44 or 45 aka 119 or 120 but anyways,
answer:
b = 2
step-by-step explanation:
because its roots are -4 and 2,
and a = 1 [The coefficient of
] we know that
using the distributive property we get,
![x^2 + 2x - 8 = 0.](https://tex.z-dn.net/?f=x%5E2%20%2B%202x%20-%208%20%3D%200.)
by equating coefficients (common strategy for partial fractions and undetermined coefficient method of solving ODE), we get b = 2 and c = -8 ( solved c just for fun guess :) ) .
hope this helps :)
<em>-audrey <3</em>
Answer:
1. 1/4 or 0.25 2.0.75
Step-by-step explanation: