Question

1. The response time of a distributed computer system is an important quality characteristic. The system manager wants to know whether the mean response time to a specific type of command exceeds 75 millisec. From previous experience, he knows that the standard deviation of response time is 4 millisec. The command is executed 25 times, and the response time for each trial is recorded. We assume that these observations can be considered as a random sample of the response times which has approximately normal distribution. The sample average response time is found as 79.25 millisec.

   1. a) Find a 95% two-sided confidence interval of the mean response time.

   2. b) Discuss what practical conclusions you would draw in part (a).

Answer 1

a)
sample mean, xbar = 79.25
sample standard deviation, σ = 4
sample size, n = 25

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

ME = zc * σ/sqrt(n)
ME = 1.96 * 4/sqrt(25)
ME = 1.57

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (79.25 - 1.96 * 4/sqrt(25) , 79.25 + 1.96 * 4/sqrt(25))
CI = (77.68 , 80.82)

b

AS the confidence interval does not contains 75, reject the null hyothesis