2. (30 points) The 96th percentile confidence interval for the response time of

Question

2. (30 points) The 96th percentile confidence interval for the response time of a database transaction system is given by the interval [3 0.4, 3 + 0.4] in seconds. This confidence interval was computed using 40 samples. Answer the following questions (stating any assumptions you make):

(a) Based on the above information, what do you think the standard deviation of the sample used to compute this confidence interval was?

(b) Compute a 99th percentile confidence interval for this system. (c) How many more samples do you need to make the 96th percentile confidence interval be [3 0.1, 3 + 0.1]?

Explanation / Answer

we consider it to be apprximaely normal as sample size is greater then 30. therefore z distribution is appropriate.

here margin of errorrE=0.4 =z*std deviation/(n)1/2 where n=40 and for 96% z=2.0537

hence std deviation =1.2318

b) for 99% ; z=2.5758

hence confidence interval =mean +/- z*std deviation/(n)1/2 =0.5017

c) for margin of error has shrunk to 1/4th times hence sample size needs to increase by 16 time.

therefore 15 more samples of size 40 is required,

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.