A sample is selected from a population with µ = 150. After a treatment is admini

Question

A sample is selected from a population with µ = 150. After a treatment is administered to the individuals, the sample mean is found to be M = 145 and the variance equal to 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 = .05. 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 = .05. c. Describe how increasing the size of the sample affects the standard error and the likelihood of rejecting the null hypothesis.

Explanation / Answer

mean, mu = 150
sample mean, M = 145
s^2 = 100, s = 10

a)
SE = s/sqrt(n) = 10/sqrt(2) = 7.0711
Test statistics, t = (145 - 150)/7.0711 = -0.7071

p-value = 0.6082

Failed to reject null hypothesis.
There are not sufficient evidence to conclude that the treatment has a significant effect

b)
SE = s/sqrt(n) = 10/sqrt(25) = 2
Test statistics, t = (145 - 150)/2 = -2.5

p-value = 0.009827088

Reject null hypothesis.
There are sufficient evidence to conclude that the treatment has a significant effect

c)
Increasing the size of sample size decreased the standard error and hence increases the likelihood of rejecting the null hypothesis.

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