The use of the interval p ± ( z critical value) requires a large sample. For eac
ID: 3225578 • 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 = 53 and p = 0.30
YesNo
(b) n = 53 and p = 0.05
YesNo
(c) n = 18 and p = 0.45
YesNo
(d) n = 104 and p = 0.02
YesNo
(e) n = 104 and p = 0.60
YesNo
(f) n = 40 and p = 0.25
YesNo
(g) n = 63 and p = 0.25
YesNo
(h) n = 84 and p = 0.10
YesNo
p(1 p) nExplanation / Answer
For interval to be appropriate, np > 5 and nq > 5
a) Both are greater than 5.
Yes
b) np = 53(0.05) = 2.65 < 5
No
c) Both are greater than 5.
Yes
d) np = 104(0.02) = 2.08 < 5
No
Similarly,
The answers for e, f, g and h would be Yes because both np and nq are greater than or equal to 5.
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