An experiment investigated the effectiveness of a nicotine l

An experiment investigated the effectiveness of a nicotine lozenge for subjects who wanted to quit smoking (Shiffman et al., 2002). Before the treatments began, subjects answered background questions, including how many cigarettes they smoked per day. Among the 1818 subjects in the study, the average was 22.0 cigarettes per day, and the standard deviation was 10.8 cigarettes per day.

a. Identify the population and parameter of interest.

Population of interest:

Parameter of interest:

b. Produce a 98 % confidence interval for the population mean number of cigarettes smoked per day.

Round your answers to four decimal places.

Solution

a)

Population of interest: All Smokers
Parameter of Interest: Population Mean number of Cigarettes per Day

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b)

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.01          
X = sample mean =    22          
z(alpha/2) = critical z for the confidence interval =    2.326347874          
s = sample standard deviation =    10.8          
n = sample size =    1818          
              
Thus,              
Margin of Error E =    0.589252555          
Lower bound =    21.41074745          
Upper bound =    22.58925255          
              
Thus, the confidence interval is              
              
(   21.41074745   ,   22.58925255   )   [ANSWER]