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Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
ISBN: 9781305504912

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BuyFindarrow_forward

Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
ISBN: 9781305504912
Textbook Problem

To evaluate the effect of a treatment, a sample of n = 8 is obtained from a population with a mean of μ = 40 , and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 35 . a. If the sample variance is s 2 = 32 , are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = .05 ?

b. If the sample variance is s 2 = 72 , are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = .05 ?

c. Comparing your answer for pans a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test?

To determine

To test for the significance of effect of treatment on a sample which results into fixed mean but for varying value of sample variance?

Explanation

Given:

a) n=8, M=35, μ=40, s2=32, a=0.05, df=7

b) n=8, M=35, μ=40, s2=72, a=0.05, df=7

Formula used:

In both the cases, for testing the significance we use t test for single mean. Firstly we define null and alternative hypothesis, which is,

Null hypothesis: Ho= there is no significant effect of the treatment.

Alternative hypothesis: H1= there is significant effect of the treatment.

OR

Null hypothesis: Ho: μ = 40

Alternative hypothesis: H1: μ 40

And then calculate the t value and check for its possible acceptance and rejection on the basis of tabulated t value of given level of significance and degree of freedom

t statistics is given by t= Mμs2n

Calculation:

a) t= Mμs2n = 3540328=52=2

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