Question

In the Seven Kingdoms of Westeros, the Night's Watch is a military order tasked with guarding the northern border from its enemies. The members of the group are highly varied in experience, with some members joining of their own volition, and others being forced to join as an alternative to incarceration or execution. Suppose that we sampled 81 members of the Night's Watch, and found that the average number of years of experience in the sample was 2.5 years, with a standard deviation of 1.1 years.

(a) Construct a 95% confidence interval for the population mean

(b) Construct a 95% confidence interval for the population mean

(c) Interpret the confidence interval you constructed in part (b).

(d) Are your intervals in this problem Z-intervals or t-intervals? Explain how you chose between the two when it was time to construct the interval.

Answer 1

Solution :-

Given :- X bar = 2.5 years , S = 1.1 years , n = 81, Df = n - 1 = 80

At 95 % Confidence level and DF = 80 , t = 1.9901.

At 95 % ,CI for Mean is

a ) Confidence Interval = ( 2.3 , 2.7 ).

b ) Confidence Interval = ( 2.3 , 2.7 ).

c ) We are 95 % confident that this interval contains the true population mean.

d ) Interval is -- t interval. The Given data contains the Sample value so the standard deviation in this is considered to be sample std deviation.