Question
A sample is selected from a population with mu = 80. After a treatment is administered to the individuals, the sample mean is found to be M = 75 and the variance is s^2 = 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. S_M = ______ t_critical = ________ t_calculated = _________ Decision = _________ 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. S_M = _________ t_critical = _________ t_calculated = ________ Decision = _________ c. Describe how increasing the size of the sample affects the standard error and the likelihood of rejecting the null hypothesis.
Explanation / Answer
Answer:
2).a).
Standard error = sd/sqrt(n)= 10/sqrt(4) =5
Df=4-1=3, t critical =3.182
(Reject Ho if t < -3.182 or t > 3.182)
t calculated = (75-80)/5= -1
Decision: Do not reject Ho.
b).
Standard error = sd/sqrt(n)= 10/sqrt(25) =2
Df=4-1=3, t critical =2.064
(Reject Ho if t < -2.064 or t > 2.064)
t calculated = (75-80)/2= -2.5
Decision: Reject Ho.
c). By increasing the sample size, the standard error decreases and increasing the likelihood of rejecting the null hypothesis.