Calculation practice: Confidence interval for the difference between two means. Return to the data about the percentage of dreams in color as a function of age from Practice Problem 2. Determine a 95% confidence interval for the difference in mean percent of color dreams between the older and younger groups.

a. If you have not done so already from the previous problem, calculate the standard error of the difference between means. (This should be the same as in part [f] of Practice Problem 2.)

b. How many degrees of freedom does the t-statistic for this analysis have?

c. For a 95% confidence interval, what value of a^a should we use?

d. Using Statistical Table C, find the critical value of t^t for this α with the correct number of degrees of freedom.

e. What is the observed difference between means ( Y̅₁− Y̅₂)

f. Calculate the 95% confidence interval for the difference between population means.

Data from problem 2

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 ttest for this comparison.