To evaluate the effect of a treatment, a sample of n = 9 is obtained from a population with a mean of μ = 40, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 33. If the sample has a standard deviation of s = 9, do we reject or accept the null hypothesis using a two-tailed test with alpha = .05?

Yes we reject the null hypothesis

Step-by-step explanation:

From the question we are told that

  The sample size is  

   The  population mean is  

    The  sample  mean is  

    The  standard deviation is

    The  level of significance is  

For a two-tailed test

The  null hypothesis is  

The alternative hypothesis is  

Generally the test statistics is mathematically represented as

=>    

=>    

The  p-value for the two-tailed test  is mathematically represented as

From the z-table  

Given that Then we reject the null hypothesis

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0