A group of friends decided to work together to decrease their cigarette smoking. They hypothesize that they can decrease their level of smoking by doing such things as giving one another encouragement, using carrots and candy to replace the physical action of smoking, and using deep breathing and counting through cravings. Each friend keeps track of how many cigarettes he or she smokes each day. The first set of data is each person's baseline (before beginning the plan), and the second set of data is after 4 weeks of using the tools. Complete the steps below to test their hypothesis.

a. For each of the two time periods, calculate the sample size \(\left(N_{i}\right)\), the mean \(\left(\bar{X}_{i}\right)\), and the standard deviation \(\left(s_{i}\right)\).

b. Calculate the mean \(\left(\bar{X}_{D}\right)\) and the standard deviation of the difference scores \(\left(s_{D}\right)\).

c. State the null and alternative hypotheses \(\left(\mathrm{H}_{0}\right.\) and \(\left.\mathrm{H}_{1}\right)\).

d. Make a decision about the null hypothesis.
(1) Calculate the degrees of freedom ( \(d f\) ).
(2) Set alpha \((\alpha)\), identify the critical values (draw the distribution), and state a decision rule.
(3) Calculate a value for the \(t\)-test for dependent means.
(4) Make a decision whether to reject the null hypothesis.
(5) Determine the level of significance.

e. Draw a conclusion from the analysis.

f. Relate the result of the analysis to the research hypothesis.

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