Answer:
CI(lower ==> xbar - a) = 9.769841
CI(upper ==> xbar + a) = 10.748909
Step-by-step explanation:
First, the standard deviation of the sample is not 9 as stated in the question. It is 0.9990493. And the mean of the observation is 10.25938.
The formula for calculation mean and standard deviation are:
Mean = [tex]\frac{\sum_{i=1}^{n} x_{i}}{n}[/tex], and
Standard deviation = [tex]\sqrt{\frac{\sum_{i=1}^{n}(x_{i} - \bar{x})^2}{n-1} }[/tex]
By Confident interval (CI),
CI = [tex]\bar{x} \pm Z_{\alpha/2} * \frac{\sigma}{\sqrt{n}}[/tex],
Where [tex]\frac{\sigma}{\sqrt{n}}[/tex] = Standard error (se), and [tex]Z_{\alpha/2} = 1.96[/tex].
If we compute this CI = [tex]\bar{x} \pm Z_{\alpha/2} * \frac{\sigma}{\sqrt{n}}[/tex], we have [9.769841, 10.748909].
For replication of answers, use the R codes below:
d = c(10.35, 9.30, 10.00, 9.96, 11.65, 12.00, 11.25, 9.58, 11.54,
9.95, 10.28, 8.37, 10.44, 9.25, 9.38, 10.85)
mean(d)
sd(d)
se = sd(d)/sqrt(length(d))
se
CIl = mean(d) - 1.96* se
CIU = mean(d) + 1.96* se
CI = c(CIl, CIU)
