Question

Suppose a simple random sample from a normal population yields the following data: x1 = 20, x2 = 5, x3 =
10, x4 = 13, x5 = 17, x6 = 18. Find a 95% confidence interval for the population mean μ.
A. [11.53, 16.13] B. [10.03, 17.63] C. [9.32, 18.34] D. [7.91, 19.75] E. other value

SHOW WORK

Answer 1

Answer:

Sample size: n= 6,  

Confidence level: c= 95%

given data is:

20, 5, 10, 13, 17, 18

now calculate the sample mean and sample standard deviation for the given data we get,

sample mean: = 13.8333

sample standard deviation: s= 5.6362

formula for confidence interval is

Where tc is the t critical value for c=95% with df=n-1 = 6-1 = 5

using t table we get critical value as

tc = 2.571

7.9185 <    < 19.748

We get confidence interval as [ 7.91 , 19.75 ]