The Midwest organization of retired oncologists and neurologists (m.o.r.o.n.) ha
ID: 3227376 • Letter: T
Question
The Midwest organization of retired oncologists and neurologists (m.o.r.o.n.) has recently taken flack from some of its members regarding the poor choice of the organization's name. The organization by law requires that more than 60% of the organization must approve a name change. Rather than convene a meeting, it is first desired to use a sample to determine if a meeting is necessary. A random sample of 50 of m.o.r.o.n.'s members were asked if they want m.o.r.o.n. To change its name. 40 if the respondents said "yes". The data was entered into the Statistix and the following output was generated. One sample proportion test Sample size= 50 Successes= 40 Proportion= .80 Null Hypothesis = p=.6 Alternative hypothesis= p> .6 Is the sample size n= 50 large enough to use this inferential procedure? A). Yes, since the central limit theorem works whenever proportions are used. B) yes, since both npo= 30> 15 and nqo= 20>15 C) yes since n>=30 D) no The Midwest organization of retired oncologists and neurologists (m.o.r.o.n.) has recently taken flack from some of its members regarding the poor choice of the organization's name. The organization by law requires that more than 60% of the organization must approve a name change. Rather than convene a meeting, it is first desired to use a sample to determine if a meeting is necessary. A random sample of 50 of m.o.r.o.n.'s members were asked if they want m.o.r.o.n. To change its name. 40 if the respondents said "yes". The data was entered into the Statistix and the following output was generated. One sample proportion test Sample size= 50 Successes= 40 Proportion= .80 Null Hypothesis = p=.6 Alternative hypothesis= p> .6 Is the sample size n= 50 large enough to use this inferential procedure? A). Yes, since the central limit theorem works whenever proportions are used. B) yes, since both npo= 30> 15 and nqo= 20>15 C) yes since n>=30 D) no The Midwest organization of retired oncologists and neurologists (m.o.r.o.n.) has recently taken flack from some of its members regarding the poor choice of the organization's name. The organization by law requires that more than 60% of the organization must approve a name change. Rather than convene a meeting, it is first desired to use a sample to determine if a meeting is necessary. A random sample of 50 of m.o.r.o.n.'s members were asked if they want m.o.r.o.n. To change its name. 40 if the respondents said "yes". The data was entered into the Statistix and the following output was generated. One sample proportion test Sample size= 50 Successes= 40 Proportion= .80 Null Hypothesis = p=.6 Alternative hypothesis= p> .6 Is the sample size n= 50 large enough to use this inferential procedure? A). Yes, since the central limit theorem works whenever proportions are used. B) yes, since both npo= 30> 15 and nqo= 20>15 C) yes since n>=30 D) noExplanation / Answer
Answer
B) yes, since both npo= 30> 15 and nqo= 20>15
Explanation
The hypothesis test for proportion using normal approximation is valid when the sample size is large enough so that
np0 15 and nq0 0
Here p0 = 0.6, n = 50
np0 = 50 * 0.6 = 30 15
nq0 = 50 * (1 - 0.6) = 50 * 0.4 = 20 15
That is, the sample size is large enough to use the normal approximation.