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A random sample of size 100 results in a sample mean of 100. The population standard deviation is known to be 35. What is the value of the standard error of the mean? O A. 5.76 O B. 1.50 O C. 2.50 O D. 9.03 O E. 3.50 The estimates below are 95% confidence interval estimates for the population mean, calculated using sample sizes of 20, 40 and 60 (not necessarily in the order they appear here). Which estimate must have been calculated using a sample size of 20? O A. (84.50; 115.50) B. (87.35; 112.65) C. (78.09; 121.91) The Department of Basic Education's earlier findings from a survey of 100 learners suggest an average travel time of 114 minutes from home to school at one of the schools of interest. Assume the population standard deviation of leaners travel time is 30 minutes. Construct a 95% confidence interval estimate for the population mean and choose the correct answer form the list of options below. . A. (106.16; 121.84) OB. (104.2; 123.8) C. (100.28; 127.72) . OD. (108.12; 119.88) E. (102.24; 125.76) A household survey based on a of sample of 50 households in a small rural village found the average household income to be R5000 with a standard deviation R1300. Construct the 99% confidence interval estimate for the population mean household income and choose the correct answer from a list of options below. A. (4711.58; 5288.42) B. (4630.47; 5369.53) C. (4525.67; 5474.33) D. (4691.69; 5308.31) E. (4507.29; 5492.71) Consider a t distribution with 18 degrees of freedom. Which one of the following statements is incorrect? A. 80% of the area under this t distribution falls between -1.330 and +1.330. B. 99% of the area under this t distribution falls between -2.878 and +2.878. C. The t value associated with a lower tail probability of 0.025 is +2.101. D. 98% of the area under this t distribution falls between -2.262 and +2.262. . E. The t value associated with a lower tail probability of 0.05 is -1.734. A simple random sample of size 28 from a normal population results in a sample mean 200 and a sample standard deviation of 50. Construct a 99% confidence interval estimate of the population mean and choose the correct answer from the list of options below. O A. (171.02; 228.98) OB. (173.82; 226.18) O c. (175.90; 224.10) O D. (175.62; 224.38) . E. (186.12; 213.88) a Consider the following application exercise from the previous assignment: Most of the schools reported a decline in the number of absences following the Education Department's Leaner Transport Program and School Nutrition Program. In sample of 90 schools from Sekhukhune district municipality, 72 schools reported a decline in the number of learners absent. Construct a 95% confidence interval estimate of the population proportion of schools that reported a decline in the number of learners absent and choose the correct answer from the list of options below. A. (0.731; 0.869) . B. (0.670; 0.850) C. (0.691; 0.909) D. (0.692; 0.828) E. (0.717; 0.883) In a sample of 36, the sample mean is 83. It is also known that the population standard deviation is 16. You are required to use this information to test the following hypothesis: Ho: > 80 H,: