A sample is selected from a population with µ = 80. After a treatment is adminis

Question

A sample is selected from a population with µ = 80. After a treatment is administered to the individuals, the sample mean is found to be M = 75 and the variance is S2 = 100.
a. If the sample has n = 4 scores, then calculate the estimated standard error and determine whether the sample is sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with alpha = .05.
b. If the sample has n = 25 scores, then calculate the estimated standard error and determine whether the sample is sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with alpha = .05.
c. Describe how increasing the size of the sample affects the standard error and the likelihood of rejecting the null hypothesis.

Explanation / Answer

a ) for n-1=4-1 =3 degree of freedom an 0.05 level of significance critical value of t =-/+ 3.1824

std error =(variance/n)1/2 =(100/4)1/2 =5

test stat t =(X-mean)/std error =(75-80)/5 =1

as test stat is not in critical region ; therefore sample is not sufficient to conclude that the treatment has a significant effect

b)

for n-1=25-1 =24 degree of freedom an 0.05 level of significance critical value of t =-/+ 2.0639

std error =(variance/n)1/2 =(100/25)1/2 =2

test stat t =(X-mean)/std error =(75-80)/2=2.5

as test stat is in critical region ; therefore sample is  sufficient to conclude that the treatment has a significant effect

c)

therefore from above we can see that increasing the size of the sample increases likelihood of rejecting the null hypothesis.

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