Question

 

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

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

          (Use a two-tailed test with α = .05).

     b) Suppose that the sample consisted of n = 25 individuals and produced a mean of 75. Repeat the

           hypothesis test at the .05 level of significance.

     c) Compare the results from part a) to part b). How does sample size influence the outcome of a

           hypothesis test?

4) A psychologist examined the effect of chronic alcohol abuse on memory. In this experiment, a standardized memory test was used. Scores on this test for the general population form a normal distribution with μ = 50 and σ = 6. A sample of n = 22 alcohol abusers has a mean score of 47. Is there evidence for memory impairment among alcoholics? Use α = .01 for a one-tailed test.

Answer 1

a) The test hypothesis is

This is a two-sided test because the alternative hypothesis is formulated to detect hypothesized mean value on either side.
Now, the value of test static can be found out by following formula:




This is a two-sided test because the alternative hypothesis is formulated to detect hypothesized mean value on either side.
Now, the value of test static can be found out by following formula:


c) Test statistic increased as we increased the number of sample size, which helped us rejecting the null hypothesis


The test hypothesis is

This is a left-tailed test because the alternative hypothesis is formulated to detect claim if mean is less than 50.0.
Now, the value of test static can be found out by following formula: