Grover, Biswas, and Avasthi (2007) studied people who had long-term delusions, and the authors were interested in whether individuals with another mental disorder had an earlier age of onset than individuals without any other mental disorder. The mean age of onset for the group with another diagnosis was 35.39 (SD = 13.77, n = 57). For the group without another diagnosis, the mean age of onset was 42.20 (SD = 17.65, n = 31).

a. Explain why an unpaired-samples t-test is appropriate for these data.

b. What is the null hypothesis for these data?

c. What is the α for this example?

d. Is a one- or a two-tailed hypothesis appropriate for this NHST?

e. Given your response to item (d), what is the appropriate alternative hypothesis for this example?

f. Calculate the degrees of freedom for the data.

g. Find the tcrit value.

h. Calculate the pooled standard deviation and the pooled variance for these data.

i. Calculate the tobs value for the data.

j. Should you reject or retain the null hypothesis?

k. Find a p-value for this example.

l. Should you worry about Type I or Type II error in this example?

m. Calculate and interpret Cohen’s d for this example.

n. Do the data in this example violate any assumptions? If so, which one(s)?

o. The statistical power for this study was 0.858. Is that sufficient power for this study? If so, what does that mean, and why is it important?