1.A random sample of n = 12 individuals is selected from a population with = 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.

Given these values, calculate or state each of the following. Show your work or explain your answer for each. (18 points total; 3 points each)

a.Null hypothesis (H_O) and alternative hypothesis (H_A) (3 points)

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b.Degrees of freedom (df) (3 points)

c.The critical t if we are doing a two-tailed test with = .05 (3 points)

(HINT: Use Table B.2 and the df you found in 4a!)

d.Sample variance (s²) (3 points)

e.Estimated standard error (s_M) (3 points)

f.t-statistic (3 points)

g.Based on our t-statistic and our critical t, is our sample significantly different from our population? How do you know? (3 points)