Answer:
(17.42 ; 22.38)
Step-by-step explanation:
To construct a confidence interval we use the following formula:
ci = (sample mean) +- z*(sd)/[n^(1/2)]
The sample mean is 19.9 and the standard deviation is 6. The sample has a n of 16. We have to find the value of z which is the upper (1-C)/2 critical value for the standard normal distribution. Here, as we want a confidence interval at a 90% we have (1-C)/2=0.05 we have to look at the 1-0.05=0.95 value at the normal distribution table, which is 1.65 approximately. Replacing all these values:
ci: (sample mean - z*(sd)/[n^(1/2)] ; sample mean + z*(sd)/[n^(1/2)])
ci: (19.9 - 1.65*6/[16^(1/2)] ; 19.9 + 1.65*6/[16^(1/2)])
ci: (19.9 - 9.9/4] ; 19.9 + 9.9/4)
ci: (19.9 - 2.48 ; 19.9 + 2.48)
ci: (17.42 ; 22.38)
