Answer:
95% confidence interval for the true mean score is [4.6 , 6.6].
Step-by-step explanation:
We are given that a sample of 81 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.
The average rating was 5.6 and the standard deviation was 4.6.
Firstly, the pivotal quantity for 95% confidence interval for the true mean is given by;
P.Q. = ~
where, = sample average rating = 5.6
s = sample standard deviation = 4.6
n = sample of tobacco smokers = 81
= population mean score
<em>Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.</em>
<u>So, 95% confidence interval for the population mean score, </u><u> is ;</u>
P(-1.993 < < 1.993) = 0.95 {As the critical value of t at 80 degree of
freedom are -1.993 & 1.993 with P = 2.5%}
P(-1.993 < < 1.993) = 0.95
P( <
<
) = 0.95
P( <
<
) = 0.95
<u>95% confidence interval for</u> = [
,
]
= [ ,
]
= [4.6 , 6.6]
Therefore, 95% confidence interval for the true mean score is [4.6 , 6.6].