5. A sample of N = 4 individuals is selected from a normal population with = 70

Question

5. A sample of N = 4 individuals is selected from a normal population with = 70 and = 10. A treatment is administered in the sample, and after the treatment, the sample mean is found to be sample mean sample mean = 75.

a. On the basis of the sample data, can you conclude that the treatment has a significant effect?

Use a two-tailedtest with = .05

b. Suppose that the sample consisted of N = 25 individuals and produced the same mean of sample mean = 75. Repeat the hypothesis z-Test at the .05 level of significance.

c. Compare the results from part a and part b. How does the sample size influence the outcome of a z-test?

Explanation / Answer

Answers to the questions:

a.

Z = (75-70)/(10/sqrt(4) = 1
A Z score of 1 means a p value of .32, which is more than alpha of .05
So, we conclude that the null hypothesis is true or "Mu=70")

b.

Z = = (75-70)/(10/sqrt(25) = 2.5
A Z score of 2.5 has a p value less than .05 ( We know 2 tailed alpha=.05 is 1.96 of Z value). So we reject null hypothesis and say that Mu!=70

c.

When sample size was increased we negated the test which in part a we didn't. i.e. made the conclusion opposite that in part a.

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