Answer: using t - test value is 1.37<2.08( At 0.05 level of significance)
The mean of the sample was drawn from the population.
Step-by-step explanation:
Here sample size n=22
Given sample mean =530
Given population mean =500
![t=\frac{sample mean-µ}{\frac{S}{\sqrt{n-1} } }](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bsample%20mean-%C2%B5%7D%7B%5Cfrac%7BS%7D%7B%5Csqrt%7Bn-1%7D%20%7D%20%7D)
given sample standard deviation s=100
<u>a) null hypothesis</u>:- The mean of the sample was drawn from the population µ =500
<u>Alternative hypothesis</u>:-
The most powerful test you can use is t - distribution.
The test statistic is
![t=\frac{sample mean- µ}{\frac{S}{\sqrt{n-1} } } here S is the standard deviation of the sampleb) The value of the test statistic [tex]t=\frac{sample mean- µ}{\frac{S}{\sqrt{n-1} } } substitute given values sample size n=22sample mean =530sample standard deviation s =100mean of the population µ =500the calculated value of t =[tex]\frac{530-500}{\frac{100}{\sqrt{22} } }](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bsample%20mean-%20%C2%B5%7D%7B%5Cfrac%7BS%7D%7B%5Csqrt%7Bn-1%7D%20%7D%20%7D%20%20%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3Ehere%20S%20is%20the%20standard%20deviation%20of%20the%20sample%3C%2Fp%3E%3Cp%3Eb%29%20%20The%20value%20of%20the%20test%20statistic%20%3C%2Fp%3E%3Cp%3E%20%20%20%20%20%20%20%20%20%20%20%20%5Btex%5Dt%3D%5Cfrac%7Bsample%20mean-%20%C2%B5%7D%7B%5Cfrac%7BS%7D%7B%5Csqrt%7Bn-1%7D%20%7D%20%7D%20%20%3C%2Fp%3E%3Cp%3Esubstitute%20given%20values%20sample%20size%20n%3D22%3C%2Fp%3E%3Cp%3Esample%20mean%20%3D530%3C%2Fp%3E%3Cp%3Esample%20standard%20deviation%20s%20%3D100%3C%2Fp%3E%3Cp%3Emean%20of%20the%20population%20%C2%B5%20%3D500%3C%2Fp%3E%3Cp%3Ethe%20calculated%20value%20of%20t%20%3D%5Btex%5D%5Cfrac%7B530-500%7D%7B%5Cfrac%7B100%7D%7B%5Csqrt%7B22%7D%20%7D%20%7D)
the calculated value=1.3748
c) The degrees of freedom =n-1 = 22-1 = 21
The table value of t are 0.05 level of significance with 21 degrees of freedom is <u>2.08</u>
The calculated value 1.37<2.08
∴ we accept null hypothesis at 0.05 level of significance
<u>conclusion:-</u>
The mean of the sample was drawn from the population.
Answer:32cm
Step-by-step explanation:
Length=L
Area=64
Area=L x L
64=L^2
L^2=64
Take them square root of both sides
√(L^2)=√(64)
L=8
Perimeter of square=4 x L
Perimeter of square=4 x 8
Perimeter of square=32
Perimeter =32cm
The answer is 3 to subtract the fractions, find the LCD and then combine
Answer:
x < 3/2 month
Step-by-step explanation:
Let
x = number of months
Planet fitness:
25 + 10x
Retro fitness:
10 + 20x
Equate
25 + 10x < 10 + 20x
25 - 10 < 20x - 10x
15 < 10x
x < 15/10
x < 3/2 month
It is less expensive to join planet when the number of months is less than 3/2 months