Question

A sample of 54 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 6.3 and the standard deviation was 4.7.
Construct a 95% confidence interval for the mean score.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 6.3

sample standard deviation = s = 4.7

sample size = n = 54

Degrees of freedom = df = n - 1 = 53

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,24 = 2.006

Margin of error = E = t_/2,df * (s /n)

= 2.006 * (4.7 / 54)

= 1.283

The 95% confidence interval estimate of the population mean is,

- E < < + E

6.3 - 1.283 < < 6.3 + 1.283

5.017 < < 7.583

(5.017 , 7.583)