Answer:
95% confidence interval for the true population mean for the amount of soda served is [12.37 , 14.23].
Step-by-step explanation:
We are given that quality control specialist for a restaurant chain takes a random sample of size 13 to check the amount of soda served in the 16 oz. serving size.
The sample mean is 13.30 with a sample standard deviation of 1.54.
Firstly, the pivotal quantity for 95% confidence interval for the true population mean is given by;
P.Q. =
~ ![t_n_-_1](https://tex.z-dn.net/?f=t_n_-_1)
where,
= sample mean = 13.30
s = sample standard deviation = 1.54
n = sample size = 13
= true population mean
<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, </u>
<u> is ;</u>
P(-2.179 <
< 2.179) = 0.95 {As the critical value of t at 12 degree of
freedom are -2.179 & 2.179 with P = 2.5%}
P(-2.179 <
< 2.179) = 0.95
P(
<
<
) = 0.95
P(
<
<
) = 0.95
<u>95% confidence interval for</u>
= [
,
]
= [
,
]
= [12.37 , 14.23]
Therefore, 95% confidence interval for the true population mean for the amount of soda served is [12.37 , 14.23].