Question

To evaluate the effect of a treatment, a sample of n=8 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=35 .

a. If the sample variance is s^2=32 , are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with alpha=.05

b. If the sample variance is s^2=72 , are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with alpha=.05 ?

c. Comparing your answer for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test?

Answer 1

Answer:

Step-by-step explanation:

a)

Test statistic:

$t=\frac{35-40}{\sqrt{\frac{32}{8} } }$

$t=-2.5$

$df=8-1=7$

$critical, t ,values=+/-2.365$

here test statistic lie in rejection region,that why null hypothesis fails  

so Yes, its significant.

b)

Test statistic:

$t=\frac{35-40}{\sqrt{\frac{72}{8} } }$

$t=-1.67$

$df=8-1=7$

$critical, t ,values=+/-2.365$

c)

sample variability increases, therefore likelihood of rejecting the null hypothesis decreases.