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madam [21]
4 years ago
5

A survey of 90 men found that an average amount spent on St. Patrick's day of $55 with a standard deviation of $18. A similar su

rvey of 86 women found they spent an average of $44 with a standard deviation of $16. When testing the hypothesis (at the 5% level of significance) that men spend more than women on St. Patrick's day, what is the test statistic?
Mathematics
1 answer:
dem82 [27]4 years ago
7 0

Answer:

The value of the test statistic is 4.70.

Step-by-step explanation:

The hypothesis for this test can be defined as follows:

<em>H</em>₀: Men do not spend more than women on St. Patrick's day, i.e. μ₁ = μ₂.

<em>H</em>ₐ: Men spend more than women on St. Patrick's day, i.e. μ₁ > μ₂.

The population standard deviations are not known.

So a <em>t</em>-distribution will be used to perform the test.

The test statistic for the test of difference between mean is:

t=\frac{\bar x_{1}-\bar x_{2}}{\sqrt{\frac{s^{2}_{1}}{n_{1}}+\frac{s^{2}_{2}}{n_{2}}} }

Given:

\bar x_{1}=55\\s_{1}=18\\n_{1}=90\\\bar x_{1}=44\\s_{1}=16\\n_{1}=86

Compute the value of the test statistic as follows:

t=\frac{\bar x_{1}-\bar x_{2}}{\sqrt{\frac{s^{2}_{1}}{n_{1}}+\frac{s^{2}_{2}}{n_{2}}} }=\frac{55-44}{\sqrt{\frac{15^{2}}{90}+\frac{16^{2}}{86} }}=4.70

Thus, the value of the test statistic is 4.70.

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Step-by-step explanation:

Given the polynomial:

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it can be reordered as follows

(x^5 + 2*x^3 + x ) + (7*x^4  + 14*x^2 + 7)

Taking greatest common factor at each parenthesis

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Taking again the greatest common factor

(x + 7)*(x^4 + 2*x^2 + 1)

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(x + 7)*(y^2 + 2*y + 1)

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Coming back to x variable

(x + 7)*(x^2 + 1)^2

There are two options to find the roots

(x + 7) = 0

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Answer:

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Step-by-step explanation:

hello :

Excluded Value :    and    

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by identity : a²-b² =(a-b)(a+b)

(x+1-4)(x+1+4) =0   so :      (x-3)(x+5) =0  means : x-3=0 or x+5=0

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Answer:

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Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    0-(1/(-x)-1+1)=0

Step by step solution :

Step  1  :

            1

Simplify   ——

           -x

Equation at the end of step  1  :

         1          

 0 -  ((—— -  1) +  1)  = 0

        -x          

Step  2  :

Rewriting the whole as an Equivalent Fraction :

2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  -x  as the denominator :

        1     1 • -x

   1 =  —  =  ——————

        1       -x  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

-1 - (x)     -x - 1

————————  =  ——————

   x           x  

Equation at the end of step  2  :

       (-x - 1)    

 0 -  (———————— +  1)  = 0

          x        

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  x  as the denominator :

        1     1 • x

   1 =  —  =  —————

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Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

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Adding fractions that have a common denominator :

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——————————  =  ——

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Equation at the end of step  4  :

      -1

 0 -  ——  = 0

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Step  5  :

Equation at the end of step  5  :

 1

 —  = 0

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Step  6  :

When a fraction equals zero :

6.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 1

 — • x = 0 • x

 x

Now, on the left hand side, the  x  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

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Equations which are never true :

6.2      Solve :    1   =  0

This equation has no solution.

A a non-zero constant never equals zero.

No solutions found

plz mark me as brainliest if this helped :)

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