The use of the interval p ± ( z critical value) requires a large sample. For eac
ID: 3135260 • Letter: T
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 = 50 and p = 0.30
YesNo
(b) n = 50 and p = 0.05
YesNo
(c) n = 15 and p = 0.45
YesNo
(d) n = 101 and p = 0.03
YesNo
(e) n = 101 and p = 0.80
YesNo
(f) n = 50 and p = 0.2
YesNo
(g) n = 60 and p = 0.2
YesNo
(h) n = 81 and p = 0.10
YesNo
p(1 p) nExplanation / Answer
The confidence interval calculations for the proportion is dependent on the following assumptions: both np 10 and n(1-p) 10.
(a)np^=50*0.30=15>10, n(1-p^)=50*0.70=35>10
Yes, the sample size is large enough for use of this interval to be appropriate.
(b) np^=50*0.05=2.5<10, n(1-p^)=50*0.95=47.5>10
No, the sample size is large enough for use of this interval to be appropriate.
(c) np^=15*0.45=6.75<10, n(1-p^)=15*0.45=8.25<10
No, the sample size is large enough for use of this interval to be appropriate.
(d) np^=101*0.03=3.03<10, n(1-p^)=101*0.97=97.97>10
No, the sample size is large enough for use of this interval to be appropriate.
(e) np^=101*0.80=80.8>10, n(1-p^)=101*0.20=20.2>10
Yes, the sample size is large enough for use of this interval to be appropriate.
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