Question

+ 0.84/4.16 points Previous Answers ASWSBE14 8.E.003. My Notes + Ask Your Teacher You may need to use the appropriate appendix table or technology to answer this question. A simple random sample of 90 items resulted in a sample mean of 60. The population standard deviation is o = 10. (a) Compute the 95% confidence interval for the population mean. (Round your answers to two decimal places.) to (b) Assume that the same sample mean was obtained from a sample of 180 items. Provide a 95% confidence interval for the population mean. (Round your answers to two decimal places.) to (c) What is the effect of a larger sample size on the interval estimate? O A larger sample size provides a larger margin of error. O A larger sample size provides a smaller margin of error. O A larger sample size does not change the margin of error.

Answer 1

-> (a) Formula for the confidence interval of mean when population mean is unknown but population Standard deviation is known :- where n = sample size o = population standard deviation De = sample mear d = choosen level of significance = (100 - Barn Confidence level) % T 4/2 = value of standard normal variable at level x/2 Hene, n=90 0 = 10 x = 60 x = ( 100 - 95)% = 5% = 0.05 T/2 = T0.025 = 1.96 :.-7./2x = 60 - 1.96x 10 = 59.93 že + Ta/2X0 = 60+ 1.96 x 10 = 62-06 Answer:- 54.93 to 02.06 Answer:- 57.93 62.06

(b) If we assume that the same sample mean Tas obtained from a sample of 180 items, then n = 180. So, the value of the confidence interval will be √180 x + T 4/2 x 7 = 60 + 1-96x 10 = 61.16 * - Tal2x = 60 - 1.96 x 10mm = 58-53. V 180 Answer: - [58.55 to 61.16)