3+2.50=P or 5.50
this doesn't matter just trying to get 20 characters
Answer:
Null hypothesis
![\mathbf{H_o: \mu = 443}](https://tex.z-dn.net/?f=%5Cmathbf%7BH_o%3A%20%5Cmu%20%3D%20443%7D)
Alternative hypothesis
![\mathbf{H_1 : \mu < 443}](https://tex.z-dn.net/?f=%5Cmathbf%7BH_1%20%3A%20%5Cmu%20%3C%20443%7D)
t = - 2.05
Degree of freedom df = 14
P-value = 0.0298
Decision rule: To reject
if significance level ∝ is greater than P-value.
Conclusion: We reject
at the level of significance ∝ = 0.1, thus there is sufficient evidence to conclude that the machine is underfilling the bags.
![H_o](https://tex.z-dn.net/?f=H_o)
Step-by-step explanation:
Given that:
Population mean
= 443
Sample size n = 15
Sample mean
= 434
standard deviation
= 17
Level of significance ∝ = 0.01
The null and the alternative hypothesis can be computed as:
Null hypothesis
![\mathbf{H_o: \mu = 443}](https://tex.z-dn.net/?f=%5Cmathbf%7BH_o%3A%20%5Cmu%20%3D%20443%7D)
Alternative hypothesis
![\mathbf{H_1 : \mu < 443}](https://tex.z-dn.net/?f=%5Cmathbf%7BH_1%20%3A%20%5Cmu%20%3C%20443%7D)
The t-test statistics can be computed as :
![t = \dfrac{\overline x - \mu }{\dfrac{\sigma }{\sqrt{n}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cdfrac%7B%5Coverline%20x%20-%20%5Cmu%20%7D%7B%5Cdfrac%7B%5Csigma%20%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![t = \dfrac{434 -443}{\dfrac{17}{\sqrt{15}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cdfrac%7B434%20-443%7D%7B%5Cdfrac%7B17%7D%7B%5Csqrt%7B15%7D%7D%7D)
![t = \dfrac{-9}{\dfrac{17}{3.873}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cdfrac%7B-9%7D%7B%5Cdfrac%7B17%7D%7B3.873%7D%7D)
t = - 2.05
Degree of freedom df = n - 1
Degree of freedom df = 15 - 1
Degree of freedom df = 14
From t distribution table; from the area in the lower tail to the left of t = -2.05 and for the degree of freedom df = 14, it is given by 0.0298
Thus, P-value = 0.0298
Decision rule: To reject
if significance level ∝ is greater than P-value.
Conclusion: We reject
at the level of significance ∝ = 0.1, thus there is sufficient evidence to conclude that the machine is underfilling the bags.
![H_o](https://tex.z-dn.net/?f=H_o)
Answer:
Ellen spent $2.40 on her lunch.
Step-by-step explanation:
Let,
x be the total amount Ellen had.
Amount spent on lunch = ![\frac{x}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D)
Amount left after lunch = ![x-\frac{x}{2}=\frac{2x-x}{2}=\frac{x}{2}](https://tex.z-dn.net/?f=x-%5Cfrac%7Bx%7D%7B2%7D%3D%5Cfrac%7B2x-x%7D%7B2%7D%3D%5Cfrac%7Bx%7D%7B2%7D)
Amount spent on movie = ![\frac{1}{2}*\frac{x}{2}=\frac{x}{4}\\](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%2A%5Cfrac%7Bx%7D%7B2%7D%3D%5Cfrac%7Bx%7D%7B4%7D%5C%5C)
Amount she has left = $1.20
Total amount = Lunch amount + Movie amount + Amount left
x = ![\frac{x}{2}+\frac{x}{4}+1.20](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%2B%5Cfrac%7Bx%7D%7B4%7D%2B1.20)
![x = \frac{2x+x+4.80}{4}\\4x=3x+4.80\\x = 4.80](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B2x%2Bx%2B4.80%7D%7B4%7D%5C%5C4x%3D3x%2B4.80%5C%5Cx%20%3D%204.80)
Amount spent on lunch =
= $2.40
Hence,
Ellen spent $2.40 on her lunch.