In a smoking cessation program, over 2000 smokers were trying to quit. With no incentives, the proportion of smokers trying to quit who are still abstaining six months later is about 0.07.
Participants in the study were randomly assigned to one of four different incentives, and the proportion successful was measured six months later. Of the 498 participants in the group with the least success, 47 were still abstaining from smoking six months later. We wish to test to see if this provides evidence that even the smallest incentive works better than the proportion of 0.07 with no incentive at all.
a. State the test hypotheses.
Do not forget to first define your parameter(s).
Also, state the direction of the test.
b. Give the notation and value of the sample statistic. Please show proof of work.
c. Use a randomization distribution above to find the p-value for this test.
P-value:
d. Give the mean and standard deviation of the normal distribution that most closely matches the randomization distribution in notation format - N(Mean,Std.Dev).
e. Use the standard error found from the randomization distribution to find the standardized test statistic. Please show proof of work.
f. Compute for the standard error using the formula from Section 6.1 as recommended in class and then find the standardized test statistic. Please show proof of work.
g. Use the p-value from part (c) to give a formal generic conclusion.
h. Finally, conclude in the context of the question.