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Furkat [3]
3 years ago
10

Use the formula to find the standard error of the distribution of differences in sample means, x¯1-x¯2. Samples of size 100 from

Population 1 with mean 95 and standard deviation 14 and samples of size 90 from Population 2 with mean 75 and standard deviation 15 Round your answer for the standard error to two decimal places. standard error = Enter your answer in accordance to the question statement
Mathematics
1 answer:
garri49 [273]3 years ago
6 0

Answer:

standard error = 2.11

Step-by-step explanation:

First we stablish the data that we have for each sample:

<u>Population 1</u>                                          <u>Population </u>2

n₁ = 100                                                     n₂ = 90

x¯1= 95                                                    x¯2 = 75

σ₁ = 14                                                        σ₂ = 15                  

To calculate the standard error of each sample we would use the formulas:

σ = σ₁/√n₁

σx¯2 =  σ₂/√n₂

Now, in order to obtain the standard error of the differences between the two sample means we combine those two formulas to obtain this:

σx¯1 - σ x¯2  = √(σ₁²/n₁ + σ₂²/n₂ )

So as you can see, we used the square root to simplify and now we require the variance of each sample (σ²):

σ₁² = (14)² = 196

σ₂² = (15)² = 225

Now we can proceed to calculate the standard error of the distribution of differences in sample means:

σx¯1 - σx¯2  = √(196/100 + 225/90) =  2.11

This gives an estimate about how far is the difference between the sample means from the actual difference between the populations means.

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Simplify u^2+3u/u^2-9<br> A.u/u-3, =/ -3, and u=/3<br> B. u/u-3, u=/-3
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  The correct answer is:  Answer choice:  [A]:
__________________________________________________________
→  "\frac{u}{u-3} " ;  " { u \neq ± 3 } " ; 

          →  or, write as:  " u / (u − 3) " ;  {" u ≠ 3 "}  AND:  {" u ≠ -3 "} ; 
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Explanation:
__________________________________________________________
 We are asked to simplify:
  
  \frac{(u^2+3u)}{(u^2-9)} ;  


Note that the "numerator" —which is:  "(u² + 3u)" — can be factored into:
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And that the "denominator" —which is:  "(u² − 9)" — can be factored into:
                                                      →   "(u − 3) (u + 3)" ;
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Let us rewrite as:
___________________________________________________________

→    \frac{u(u+3)}{(u-3)(u+3)}  ;

___________________________________________________________

→  We can simplify by "canceling out" BOTH the "(u + 3)" values; in BOTH the "numerator" AND the "denominator" ;  since:

" \frac{(u+3)}{(u+3)} = 1 "  ;

→  And we have:
_________________________________________________________

→  " \frac{u}{u-3} " ;   that is:  " u / (u − 3) " ;  { u\neq 3 } .
                                                                                and:  { u\neq-3 } .

→ which is:  "Answer choice:  [A] " .
_________________________________________________________

NOTE:  The "denominator" cannot equal "0" ; since one cannot "divide by "0" ; 

and if the denominator is "(u − 3)" ;  the denominator equals "0" when "u = -3" ;  as such:

"u\neq3" ; 

→ Note:  To solve:  "u + 3 = 0" ; 

 Subtract "3" from each side of the equation; 

                       →  " u + 3 − 3 = 0 − 3 " ; 

                       → u =  -3 (when the "denominator" equals "0") ; 
 
                       → As such:  " u \neq -3 " ; 

Furthermore, consider the initial (unsimplified) given expression:

→  \frac{(u^2+3u)}{(u^2-9)} ;  

Note:  The denominator is:  "(u²  − 9)" . 

The "denominator" cannot be "0" ; because one cannot "divide" by "0" ; 

As such, solve for values of "u" when the "denominator" equals "0" ; that is:
_______________________________________________________ 

→  " u² − 9 = 0 " ; 

 →  Add "9" to each side of the equation ; 

 →  u² − 9 + 9 = 0 + 9 ; 

 →  u² = 9 ; 

Take the square root of each side of the equation; 
 to isolate "u" on one side of the equation; & to solve for ALL VALUES of "u" ; 

→ √(u²) = √9 ; 

→ | u | = 3 ; 

→  " u = 3" ; AND;  "u = -3 " ; 

We already have:  "u = -3" (a value at which the "denominator equals "0") ; 

We now have "u = 3" ; as a value at which the "denominator equals "0"); 

→ As such: " u\neq 3" ; "u \neq -3 " ;  

or, write as:  " { u \neq ± 3 } " .

_________________________________________________________
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