In: Statistics and Probability
We’re interested in studying the effect of physician encouragement on a smoker’s decision to quit. A study was conducted where an SRS of 114 smokers were, during routine exams, told about the hazards of smoking and encouraged to quit by the examining physician. A different SRS of 96 smokers were given no advice pertaining to smoking during their routine examination. Of the smokers who received physician encouragement, 11 quit. Of the smokers who received no physician encouragement, 7 quit. Use this information to answer the following.
(a) Find and interpret a 95% confidence interval for the difference in true proportions of quitting smoking between those who receive encouragement to quit from their physicians and those who do not. Check that the necessary conditions are met.
(b) Check the conditions required to perform a hypothesis test for this data to test if there is a difference in the proportions of quitters. Using your answer to part (a), make a formal conclusion. At what level of significance can you make this conclusion?