Question

Calculate the lower confidence limit (LCL) and upper confidence limit (UCL) of the mean for each of the following a. x = 455, n = 348, ?-20, and ? = 0.05 b.x-85, n = 184, ?2 = 49, and ? = 0.01 ER Click the icon to view the standard normal table of the cumulative distribution function. a. LCL= | | (Round to two decimal places as needed.) UCL= ? (Round to two decimal places as needed.) b, LCL=? (Round to two decimal places as needed.) UCL= ? (Round to two decimal places as needed.)

Answer 1

95% CI for μ using Normal dist Sample Mean-455 Population Standard deviation = σ = 20 Sample Size -n- 348 Significance level-α-1-Confidence-1-0.95-0.05 The Critical Value -Za/220.025 1.96 (From z table) Critical Values,z/1.96 Margin of Error-E·α/2 × Margin of Error, E= 2.101 202.101341 348 1 Vn Limits of 95% confidence interval are given by: Lower limit -- E 4552.101341452.898659 452.90 Upper limitE 455+2.101341 457.101341457.10 95% confidence interval is: x - (452.898659, 457.101341) E-455士2.101341 95% CI using normal dist: 452.90 < μ < 457.10 Also, the exact answer using TI-83/84 or excel is 455 t invNorm(0.975) x 20/sqrt(348) (452.8986971326, 457.101 3028674)

99% CI for μ using Normal dist Sample Mean 85 Population Standard deviation-σ-νσ2-V49-7 Sample Size -n- 184 Significance level-α-1-Confidence-1-0.99-0.01 The Critical Value- 2a/2 20.005 2.58 (closest value From z table) Critical Values ,za/22.58) Note that some professors take z0.005 2.575 Margin of Error-E-za/2 1.331401 184 Margin of Error, E 1.331 Limits of 99% confidence interval are given by: Lower limit E-85-1.331401 83.668599 Upper limitE 85 1.331401 86.331401 83.67 86.33 99% confidence interval is: x - (83.668599, 86.331401) E-85士1.331401 99% CI using normal dist: 83.67 < μ < 8633 Also, the exact answer using TI-83/84 or excel is 85士invNorm(0.995) × 7/sqrt(184) (83.6707510154, 86.3292489846) @seoThank ,youJ0户