A sample of 132 tobacco smokers who recently completed a new smoking-cessation program were asked to rate the effectiveness of the program on a scale of 1 to 10, with 10 corresponding to "completely effective" and 1 corresponding to "completely ineffective". The average rating was 5.7 and the standard deviation was 4.7.
Construct a 95% confidence interval for the mean score
A) $( 5.3,6.1 )$
B) $( 0,5.7 )$
C) $( 4.9,6.5 )$
D) $( 5.4,6.0 )$

Question

Quizplus · Accepted Answer

To construct a 95% confidence interval for the mean score, we use the formula: $\bar{x} \pm z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the confidence level (for 95%, $z = 1.96$), $\sigma$ is the standard deviation, and $n$ is the sample size. Plugging in the values: $5.7 \pm 1.96\frac{4.7}{\sqrt{132}}$, we get the interval $(4.9, 6.5)$.

A Sample of 132 Tobacco Smokers Who Recently Completed a New