The superintendent of a large school district, having once had a course in probability and statistics, believes that thenumber of teachers absent on any given day has a Poisson distribution with parameter u. Use the accompanying data onabsences for 50 days to obtain a 95% large-sample CI for u.Number ofabsences0 1 23 4 5 6 7 8 9 10Frequency1 3 7 12 875 4 1 1[Hint: The mean and variance of a Poisson variable both equal u, soZ =V H/nhas approximately a standard normal distribution. Now proceed as in the derivation of the interval for p by making aprobability statement (with probability 1 -a) and solving the resulting inequalities for u.] (Round your answers to twodecimal places.)

Provided data is: No. of absence Frequency 0 1 1 3 2 7 3 12 4 8 5 7 6 5 7 4 8 1 9 1 10 1 Provided data has poisson distribution with parameter µ.mean of the data can be calculated as: x=∑i=nfxi∑i=1nfi No. of absence Frequency fx 0 1 0 1 3 3 2 7 14 3 12 36 4 8 32 5 7 35 6 5 30 7 4 28 8 1 8 9 1 9 10 1 10 Ʃf=50 Ʃfx=205 Thus, mean is: x=20550=4.1 For poisson distribution, mean of the data and variance both are equal. µ=σ=4.1From provided information, Z=x-μμ/σ follows normal distribution. Probability statement of interval can be given as: P-Zα/2<x-μμ/n<Zα/2 Each inequality symbol is replaced by equal to sign and solving equation for µ, obtained two roots are: CI for μ=x+Zα/222n±Zα/22n4x¯n+Zα/22 For 95% confidence level, Zα/2=1.96 Calculated from standard normal table. Thus, 95% confidence interval is: CI=4.1+1.962250±1.9625044.150+1.962=3.5758,4.7010 Thus, 95% confidence interval for µ is (3.58, 4.70).

Math

Statistics

has approximately a standard normal distribution. Now proceed as in the derivation of the interval for p by making a probability statement (with probability 1 – a) and solving the resulting inequalities for u.] (Round your answers to tw decimal places.)

has approximately a standard normal distribution. Now proceed as in the derivation of the interval for p by making a probability statement (with probability 1 – a) and solving the resulting inequalities for u.] (Round your answers to tw decimal places.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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