Question

To evaluate the effect of a treatment, a sample of n = 6 is obtained from a population with a mean of μ = 80 and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 72. a. If the sample variance is s2 = 54, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α =0.05? b. If the sample variance is s2 = 150, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α =0.05? c. Comparing your answers for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test?

Answer 1

part(a)
Given that,
population mean(u)=80
sample mean, x =72
standard deviation, s =sqrrt(54) = 7.348
number (n)=6
null, Ho: μ=80
alternate, H1: μ!=80
level of significance, alpha = 0.05
from standard normal table, two tailed t alpha/2 =2.571
since our test is two-tailed
reject Ho, if to < -2.571 OR if to > 2.571
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =72-80/(7.348/sqrt(6))
to =-2.6668
| to | =2.6668
critical value
the value of |t alpha| with n-1 = 5 d.f is 2.571
we got |to| =2.6668 & | t alpha | =2.571
make decision
hence value of | to | > | t alpha| and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -2.6668 ) = 0.0445
hence value of p0.05 > 0.0445,here we reject Ho
sufficient to conclude that the treatment has a significant effect using a two-tailed test
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part(b)
standard deviation, s =sqrt(150) 12.247
to =72-80/(12.247/sqrt(6))
to =-1.6001
| to | =1.6001
critical value
the value of |t alpha| with n-1 = 5 d.f is 2.571
we got |to| =1.6001 & | t alpha | =2.571
make decision
hence value of |to | < | t alpha | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -1.6001 ) = 0.1705
hence value of p0.05 < 0.1705,here we do not reject Ho
no sufficient to conclude that the treatment has a significant effect using a two-tailed test
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part(c)
increasesing the the variability of the scores in the sample influence the outcome of a hypothesis