A sample of 125 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 4.1 and the standard deviation was 4.0.
Construct a 95% confidence interval for the mean score.
A) $3.8

Question

A sample of 125 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 4.1 and the standard deviation was 4.0.
Construct a 95% confidence interval for the mean score. 
A) $3.8 < \mu < 4.4$
B) $0 < \mu < 4.1$
C) $3.4 < \mu < 4.8$
D) $3.7 < \mu < 4.5$

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 given values: $4.1 \pm 1.96 \frac{4.0}{\sqrt{125}}$, we get the interval $3.4 < \mu < 4.8$.

A Sample of 125 Tobacco Smokers Who Recently Completed a New