Question

A study reported in Newsweek (December 23, 1991) involved a sample of 935 smokers. Each individual received a nicotine patch, which delivers nicotine to the bloodstream but at a much slower rate than cigarettes do. Dosage was decreased to 0 over a 12-week period. Suppose that 245 of the subjects were still not smoking 6 months after treatment (this figure is consistent with information given in the article). Estimate the percentage of all smokers who, when given this treatment, would refrain from smoking for at least 6 months.

Short answer

The estimated percentage of all smokers who, when given this treatment, would refrain from smoking for at least 6 months is \( 26.2\% \).

Step-by-step solution

Identify the Relevant Sample and Outcome

The total number of smokers in the sample is 935, and the number of those who were successful in refraining from smoking for at least 6 months after the treatment is 245. These will be used to calculate the proportion.

Calculate the Proportion

The proportion of succeeding smokers can be calculated by dividing the number of successful outcomes by the total sample size, then multiplying by 100 to get the percentage. Thus, the formula is as follows: \( Proportion = \frac{Number\: of\: successes}{Total\: sample\: size} \times 100 \)

Substitute the Known Values

Now, substitute the values into the formula: \( Proportion = \frac{245}{935} \times 100 \)

Compute the Answer

Perform the calculations to get the final proportion. This represents an estimate of the percentage of all smokers who, when given this treatment, would refrain from smoking for at least 6 months.