The use of the interval p ± ( z critical value) requires a large sample. For eac

Question

The use of the interval

p ± (z critical value)

requires a large sample. For each of the following combinations of n and p, indicate whether the sample size is large enough for use of this interval to be appropriate.

(a)    n = 55 and p = 0.30

YesNo    

(b)    n = 55 and p = 0.05

YesNo    

(c)    n = 11 and p = 0.45

YesNo    

(d)    n = 110 and p = 0.01

YesNo    

(e)    n = 110 and p = 0.80

YesNo    

(f)    n = 50 and p = 0.2

YesNo    

(g)    n = 65 and p = 0.2

YesNo    

(h)    n = 90 and p = 0.10

YesNo   

p(1 p) n

Explanation / Answer

np > 5 and n(1-p) > 5

then sample size is large enough

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n p np n(1-p) Result 55 0.3 16.5 38.5 yes 55 0.05 2.75 52.25 no 11 0.45 4.95 6.05 no 110 0.01 1.1 108.9 no 110 0.8 88 22 yes 50 0.2 10 40 yes 65 0.2 13 52 yes 90 0.1 9 81 yes

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