Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Confidence Interval Mean, σ known, n > 30 A certain medication is known to increase the pulse rate of its users. The standard deviation of the pulse rate is known to be 5 beats per minute from previous studies. A sample of 55 users had an average pulse rate of 104 beats per minute. Find the 99% confidence interval of the true mean. First by calculation: Since we need the 99% confidence interval we have α = 0.01 and since we may be in error either high or low we need to split α and find Zα = 2.575 . 2 € 0.005 0.005 Zα = −2.575 Zα = 2.575 2 2 ⎛ σ ⎞ ⎛ 5 ⎞ Z = 2.575 Our error term is E = ⎜ ⎟ ⎜ ⎟ = 1.736064646 so the € € α 2 ⎝ n ⎠ ⎝ 55 ⎠ interval is: x−E <µ<x+E 102.3 < µ < 105.7 € ⇒€ 104 – 1.7 < µ < 104 + 1.7 Now using the calculator to find this interval. Press Stat € ← Select Stats σ: 5 x :104 n: 55 C-Level:0.99 Calculate ZInterval (7) ZInterval (102.26,105.74) x :104 n:55 ⇒ € So 102.26 < µ < 105.74