A sample of 69 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 4.5
And the standard deviation was 4.3.
Construct a 95% confidence interval for the mean score.
A) (4.0, 5.0)
B) (0, 4.5)
C) (3.5, 5.5)
D) (4.1, 4.9)

Question

Quizplus · Accepted Answer

We can use the formula for a confidence interval for the mean:

Confidence interval = sample mean ± (t-score)*(standard error of the mean)

First, we need to find the t-score with 68 degrees of freedom (n-1) and a 95% confidence level. Using a t-table or calculator, we find the t-score to be approximately 1.998.

Next, we need to find the standard error of the mean:

standard error of the mean = standard deviation / sqrt(sample size)
standard error of the mean = 4.3 / sqrt(69)
standard error of the mean ≈ 0.52

Plugging in the values, we get:

Confidence interval = 4.5 ± (1.998)*(0.52)
Confidence interval ≈ (3.474, 5.526)

Therefore, the 95% confidence interval for the mean score is (3.5, 5.5), which corresponds to choice C.

A Sample of 69 Tobacco Smokers Who Recently Completed a New