The \"z-i, u rene\" Mave? Linking Risks-Tsinth Defects with thhe state of New Je

Question

The "z-i, u rene" Mave? Linking Risks-Tsinth Defects with thhe state of New Jensey e s al w eey eiots who live within 1 mile of a wwximaely norssal distriucion? Esplain asf nyyse thasp-03 stiple of silems have an h What would be the misimum ssmple sice m sample sine have to be in order to assure anm epyrosximately soal dirin for the sampling of proportions _ntimately rmaldistributum fnr the sampling of proporo e Betermaine the sampling diseribuains of the sample peupotions of sine 400 d) When n- 400, what is Py 25 sps35) e) Is the probability calculated in part (d) larger or case if 500. Without doing the computation, explain smaller than would be the your reasoning? Based on a sample selected at random over the past 6 months, a dentist has seen the ollowing number of patients per wek: 22,25,20, 17, 19, 22, 24, 22, 19 and 26. ssume that the number of patients seen per week is normally distributed. a) Provide a 99.8% confidence intenal f

Explanation / Answer

a) np > 5

nq > 5

here p = 0.34 , q = 0.66

if n = 10

np = 10*0.34 = 3.4 < 5

hence normal approximation is not appropriate

b) let the minimum sample size be n

n*0.34 > 5 , n *0.66 > 5

hence n > 5/0.34 >14.705

henc n = 15

c)

when n = 400

p^ have normal distribution with mean = 0.34

and sd =sqrt(pq/n) = sqrt(0.34*0.66/400) = 0.02368543

d)

P(0.25 < p < 0.35)

=

P ( 3.8<Z<0.42 )=0.6627

e) when n= 500

variance will be smaller , hence probability will increase

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