Question

A smoking cessation program for long-term smokers claimed a relapse rate of 60% in rural settings, thought to be acceptable. A health organization wanted to test the program in a city setting and proceeded to set up a trial. The health organization formulated the following null, Ho, and alternative, H1, hypotheses to reflect their presumption that the relapse rate in the city would be higher. The symbol p below denotes the proportion of smokers who relapse. Ho:p=0.60 H:p > 0.60 The health organization recruited a random sample of 100 long-term smokers who were willing to participate in the cessation program. After one year, they found that 68 participants had relapsed. The sample statistics are summarized as follows. Sample Sample Sample Standard One-sample size count proportion error z-statistic SE 100 68 0.68 0.04899 1.6330 The next step in the analysis is to obtain the P-value. Use software to determine the P-value of the one-sample z-statistic. You might find this list of software manuals useful. Give your answer as a decimal precise to four decimal places. P=

Answer 1

The statistic software output for this problem is:

One sample proportion summary hypothesis test: p Proportion of successes Ho p 0.6 HA p 0.6 Hypothesis test results: Proportion Count Total Sample Prop. Std. Err P-value Z-Stat 68 100 0.68 0.048989795 1.6329932 0.0512

P = 0.0512