The Alpha Cola Company conducted a study to test the claim that, since each 12-ounce (by volume) can contains the same amount of cola, the mean weight of the cola in cans of regular Alpha-Cola is the same as the mean weight of the cola in cans of Diet Alpha-Cola. Five cans of regular Alpha-Cola were pulled off the production line and the mean weight (in pounds) of the cola per can was 0.82, with a standard deviation of 0.04. Four Diet Alpha-Cola cans were pulled off the production line and the mean weight (in pounds) of the cola per can was 0.78, with a standard deviation of 0.01.
Using 0.05 level of significance (p < 0.05): is the mean weight of regular Alpha-Cola the same as the mean weight of Diet Alpha-Cola?
a. State the research/alternate hypothesis and the null hypothesis.
b. Identify the characteristics of the comparison distributions; specifically, their sample means and sample standard deviations, and the quantities used to derive these.
c. Determine correct distribution, then use level of significance to determine either α or cutoff score(s).
d. Determine either the p-value or the sample statistic.
e. Determine whether to reject/fail to reject the null hypothesis, AND state the result of the test (either research hypothesis supported, or study is inconclusive).