Assume that a treatment really does have an effect and that the treatment effect
ID: 3174688 • Letter: A
Question
Assume that a treatment really does have an effect and that the treatment effect is being evaluated with a hypothesis test. If all other factors are held constant, how is the outcome of the hypothesis test influenced by sample size? To answer this question, do the following two tests and compare the results. For both tests, a sample is selected from a normal population distribution with a mean of = 60 and a standard deviation of = 10. After the treatment is administered to the individuals in the sample, the sample mean is found to be 65. In each case, use a two-tailed test with = .05. a. For the first test, assume that the sample consists of n = 4 individuals. b. For the second test, assume that the sample consists of n = 25 individuals. c. Explain how the outcome of the hypothesis test is influenced by the sample size.
Explanation / Answer
for 0.05 level ; rejection region are z>1.96 and z<-1.96
1st case
std error =std deviation/(n)1/2 =5
hence test stat z=(X-mean)/std error =(65-60)/5 =1
as z falls inside acceptance region we can not reject null hypothesis
2nd case
std error =2
test stat =(65-60)/2 =2.5
as z falls in rejection region we reject null hypothesis
c) as sample size increase; std error decreases whcich follows with reduced margin of error.