Question

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A random sample of n = 12 individuals is selected from a population with µ = 70, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 74.5 with SS = 297. Is there evidence to indicate that your sample is significantly different from the population using α=.05? calculate the effect size for your results.

Answer 1

(i)

H0:Null Hypothesis: = 70 ( our sample is not significantly different from the population )

HA: Alternative Hypothesis: 70 ( our sample is significantly different from the population ) (Claim)

n = 12

= 74.5

= 0.05

df = 12 -1 = 11

From Table, critical values of t = 2.201

Test Statistic is given by:

Since calculated value of t = 3.00 is greater than critical value of t = 2.201, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that our sample is significantly different from the population.

(ii)

the effect size for our results is got as follows:

So,

Answer is:

0.8660