Question

Suppose that you were trying to determine if out of the Americans that smoke, the proportion that have tried to quit was more than 80%. You decide to test the null hypothesis Ho: p = 0.80 versus Ha: p > 0.80. In 1994, the General Social Survey had a question that asked its participants (that currently smoked) if they had ever tried to quit smoking. Out of 142, 117 said yes, they had tried to quit smoking. Define the parameter.

A. p = the population proportion of the 142 Americans who smoked that said that they had ever tried to quit in 1994

B. phat = the population proportion of Americans who smoked that said that they had ever tried to quit in 1994

C. p = the population proportion of Americans who smoked that said that they had ever tried to quit in 1994

D. phat = the population proportion of the 142 Americans who smoked that said that they had ever tried to quit in 1994

Answer 1

Answer is C. Because you are concerned about the American smokers that had ever tried quit smoking. You asked 142 such Americans thus 142 is your sample size. Statistical hypothesis is about stating assumption on the population, specifically on the population characteristic. Hence your hypothesis can not be about 142 such Americans. Hence options A and D are ruled out. Further for notational convenience, an alphabet is used for denoting a parameter and hat of that is used for denoting its estimate. Hence we should use 'p' rather than 'phat' to denote our parameter of interest. Thus option B is ruled out and option C seems to be appropriate.