A car buyer wanted to compare prices of 3-year-old BMW and Mercedes Benz automobiles, and found these prices (in thousands of dollars) listed in the classified ads:
a. Use software to produce sample means and standard deviations of prices.
b. Are the standard deviations similar enough that we can assume they arise from populations that share the same standard deviation?
c. Use software to carry out a pooled two-sample t test (assuming equal population variances); report the test statistic t and the P-value.
d. Use software to carry out an ANOVA (F) test, which requires the assumption of equal population variances; report the test statistic F and the P-value.
e. If sample sizes and standard deviations are equal, the F statistic is in fact the square of the twosample t statistic. Find the square of your t statistic from part (c), and comment on whether or not it is about the same as the F statistic.
f. Comment on whether or not the P-values are similar for the pooled two-sample test compared to the ANOVA (F) test.
g. Comment on whether or not the P-values would be similar if the two-sample test had been carried out with a one-sided instead of two-sided alternative.