The safety commissioner in a large city wants to estimate the proportion of buil

Question

The safety commissioner in a large city wants to estimate the proportion of buildings in the city that are in violation of fire codes. A random sample of 80 buildings is chosen for inspection, and 16 of them are found to have fire code violations. Estimate the proportion of buildings in the city that have fire code violations, and find the uncertainty in the estimate to three decimal places. Particles are suspended in a liquid medium at a concentration of 7 particles per ml. A large volume of the suspension is thoroughly agitated; then 2 ml are withdrawn. What is the probability that exactly 11 particles are withdrawn? Lifetimes of batteries in a certain application are normally distributed with mean 47 hours and standard deviation 2 hours. Find the 25 th percentile of battery lifetimes. A group of workers exposed to high levels of CO were categorized on the basis of work shift and symptoms A Chi-square test was run on this data and yielded the value x^2 = 17.57 (a) What was the null hypothesis being tested (b) What was the associated p-value (c) What is the value expected in the (weakness, evening) cell?

Explanation / Answer

Q.21 Total sample size N = 80

Fire code violations = 16

proportion of fire code violations p = 16//80 = 0.2

Uncertainity or say standard deviation of the proportion = sqrt (p(1-p) * N )= sqrt (0.2 * 0.8 * 80 )= 12.8 = 3.58

Q.23 Expected number of particles in the 2 ml liquid medium = 14 particles

Pr ( exactly 11 are drawn) = we will calculate it from poisson caculator where  = 14

so Pr( X=11) = e-14 (14)11/ 11! = 0.0843

Q.24 We have to calculate 25 percentile

Pr( X< = x ; 45 ; 2) = 0.25

so from Z table P- value = - 0.675

so (x -45)/2 = -0.675

X = 45 - 2 * 0.675 = 43.65

Q. 25

Null Hypothesis : Symptoms are independent of time of work shift.

(b) p - value = the criticla value of 17.57 for dF =6 lies between 0.010 and 0.005 and by using calculator we find its value = 0.0071.

(c) Expected Table

so Value expected for ( weakness, evening) = 13.60

Morning Evening Night total Influeza 16.32 19.98 10.69 47 Headache 21.88 26.78 14.34 63 Weakness 11.11 13.60 7.28 32 Breath 8.68 10.63 5.69 25 Total 58 71 38 167

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