A random sample of n 25 individuals is selected from a population with 20 and a

Question

A random sample of n 25 individuals is selected from a population with 20 and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M 22.2 with SS 384. a. How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.) b. If there is no treatment effect, how much difference is expected between the sample mean and its population mean? That is, find the standard error for M. (Note: In a hypothesis test, this value is the denominator of the t statistic.) c. Based on the sample data, does the treatment have a significant effect? Use a two tailed test with a 05

Explanation / Answer

(a) This is x-bar - = 22.2 - 22 = 2.2

(b) This is s/n

s = (384/24) = 4

s/n = 4/25 = 0.80

(c) t = (x-bar - )/SE = (22.2 - 20)/0.8 = 2.75

p- value = 0.01114783

Since 0.011 < 0.05, we reject Ho

The treatment has a significant effect.

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