The use of the interval P plusminus (z critical value) Squareroot P(1 - P)/n req

Question

The use of the interval P plusminus (z critical value) Squareroot P(1 - P)/n 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 Yes No (b) n = 53 and p^= 0.05 Yes No (c) n = 13 and p^= 0.45 Yes No (d) n = 106 and p^= 0.03 Yes No (e) n = 106 and p^= 0.70 Yes No (f) = 40 and p^= 0.25 Yes No (g) n = 63 and p^= 0.25 Yes No (h) n = 86 p^= 0.10 Yes No In a survey of 495 potential jurors, one study found that 350 were regular watchers of at least one crime-scene forensics television series.

Explanation / Answer

Solution:

a)np hat=53*0.30=15.9>10

np hat*(1-p hat)=53*0.30*0.70=11.13>10

option Yes

b) n = 53 and p = 0.05

np hat=53*0.05=2.65<10

np hat*(1-p hat)=53*0.05*0.95=2.518<10

option No

c) n = 13 and p = 0.45

np hat=13*0.45=5.85<10

np hat*(1-p hat)=13*0.45*0.55=3.217<10

option No

d) n = 106 and p = 0.03

np hat=106*0.03=3.18<10

np hat*(1-p hat)=106*0.03*0.97=3.084<10

option No

e) n = 106 and p = 0.70

np hat=106*0.70=74.2>10

np hat*(1-p hat)=106*0.70*0.3=22.26>10

option Yes

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.