Q1 Find the sample size such that the probability of the sample means differing from the population mean by not more than 1/10th of the S.D. is 0.95. a 300 b 384 c 395 d none
6 Replies
Tejaswi Kasturi
(student-cpt)
(427 Points)
Replied 05 June 2012
Standard error = σ/√n the sampling mean for large values of n follows a normal distribution so for 0.95 certainty the population mean should be inside sample mean +/- 1.96*standard error
so 1.96*SE = σ/10 implies 1.96/ √n = 0.1 implies √n = 19.6 implies n = 19.62 = 384.16 = 384 so answer is b
Tejaswi Kasturi
(student-cpt)
(427 Points)
Replied 05 June 2012
for normal distribution there are z tables which tell you how much percentage of values fall in between x standard deviations from mean. for 95% of values to fall between mean and standard deviation, the length of the interval will be mean +/- 1.96 standard deviations.
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