A random sample of n = 16 scores is obtained from a population with a mean of µ = 80 (assume ? is unknown) and a treatment is administered to the sample. After treatment, the sample mean is found to be M = 82 (assume higher numbers mean the person's symptoms are improving) with a standard deviation of s = 8. Using a single sample t-test, evaluate the hypothesis that the treatment had an effect.
a. Using symbols, state the hypotheses (H0 and H1) for a two-tailed test.
b. Find the critical value/region for an ? = .05 for a two-tailed test.
c. Calculate the test statistic (t-statistic) for the sample.
d. Make a decision and write a conclusion statement for your result.