Question

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Question 3 (4 marks) Part a) Given the following information X-500, σ=12, n=50 i) Determine the 95% confidence interval estimate of population mean. ii) Determine the 99% o confidence interval estimate of population mean Part b) A statistics practitioner calculated the mean and standard deviation from a sample of 51. They are X-120 and s-15. (i) Estimate the population mean with 95% confidence level (ii) Estimate the population mean with 99% confidence level.

Answer 1

Answer Date: 30/01/2019 a) interval estimate of population mean is, The 95% confidence First, compute z-critical value then find confidence interval. From the standard normal table, the z-critical value at 95% confidence is 1.96. - 500 - 500 +1.96 x12/50 3.33 496.67 to 503.33 The 95% confidence interval estimate ofpopulation mean is 496.67 to 503.33

The 99% confidence interval estimate First, compute z-critical value then find confidence interval. From the standard normal table, the z-critical value at 99% confidence i s 2.575. of population mean is, 500+2.575 x12/50 -500 4.37 - 495.63 to 504.37 The 99% confidence interval estimate ofpopulati on m ean is 495.63 to 504.37 b) confidence interval estimate of population mean is, The 95% First, compute t-critical value then find confidence interval. The t critical value for the 95% confidence interval is.

The sample size is small and two-tailed test. Look in the column headed α-005 and the row headed in the t distribution table by using degree of freedom is, d.f.-n-1 - 51-1 - 50 The t critical value for the 95% confidence interval is 2.009. 95% CI.ltt.* s/./n -120 2.009 x15/V51 - 120 +4.22 - 115.78 to 124.2.2 The 95% confidence interval for the population mean is L 15.78 to 124.22 The 99% confidence interval estimate of population mean is, First, compute t-critical value then find confidence interval