Question

1. A random sample of 50 calls initiated on cell car phones had a mean duration of 3.5 Assume the population SD 671.2 min. a) Find a 95% confidence interval for the population mean duration of telephone calls initiated on cell car phone and interpret your result ) Find a 90% confidence interval for the population mean duration of telephone calls itiated on cell car phone. Compare with the result in part a)

Answer 1

Solution: n 50 x = 3.5 σ = 1.2 Part-A Confidence level = 95% α 1-0.95 0.05 a/2 0.05/2 0.025 From normal distribution table, Za/2-Z0.02 5-1.96 The 95% confidence interval estimate for population mean duration μ 1.96 σ Vn 1.96 × 1.2 1.96 × 1.2 V50 → 3.5 V50 SAS 3.5+ 3.167 μ 3.833 Hence, 95% confidence interval is-(3.167, 3.833)

Part-B: Confidence level = 90% α = 1-0.90 = 0.10 a/2 0.10/2 0.05 From normal distribution table; Za/2- Z0.05 1.645 The 90% confidence interval estimate for population mea n duration μ 1.645 × σ 1.645 × σ Vn 1.645 x 1.2 1.645× 1.2 3.5 V50 SH S 3.5+ V50 3.221 su 3.779 Hence, 90% confidence interval is-(3.221, 3.779)