A sample is selected from a population with mu = 80. After a treatment is admini

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.

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