Calculation practice: two-sample t-test. When your authors were growing up, it was thought that humans dreamed in black and white rather than color. A recent hypothesis is that North Americans did in fact dream in black and white in the era of black-and-white television and movies, but that we shifted back to dreaming in color after the introduction of color media. To test this hypothesis, Murzyn (2008) queried 30 older individuals who had grown up in the black-and-white era and 30 younger individuals who grew up with color media about their dreams. She recorded the percentage of color dreams for each individual. A mean of 68.4% of the younger peoples’ dreams were in color (with a standard deviation of 31.8%). On average, 33.9% of the older individuals’ dreams were in color, with a standard deviation of 36.9%. The scores were approximately normally distributed in each group. Is the difference between the two means statistically significant? We’ll use a two-sample t-test for this comparison.

a. State the null and alternate hypotheses for this test.

b. What are the assumptions of a two-sample t-test ? Do these data match these assumptions well enough?

c. What are the sample variances for each group?

d. How many degrees of freedom are associated with each group?

e. Calculate the pooled variance for these data.

f. What is the standard error of the difference between means?

g. Calculate t.

h. How many degrees of freedom does this t-statistic have?

i. What is the critical value of t with α=0.05 for this test?

j. What is the most precise P-value that you can determine for this test?

k. What can you conclude about the difference between the older and younger people in how often they dream in color? Interpret the conclusions of the test in terms of the original scientific question.