A certain chromosome defect occurs in only 1 in 190 adult Caucasian males. A ran

Question

A certain chromosome defect occurs in only 1 in 190 adult Caucasian males. A random sample of n = 100 adult Caucasian males is to be obtained. (a) What is the mean value of the sample proportion and what is the standard deviation of the sample proportion? (Enter your mean as an exact integer, fraction, or decimal. Round your standard deviation to five decimal places.) mean standard deviation (b) Does p have approximately a normal distribution in this case? Explain. Yes, because np 10. No, because np 10. (c) What is the smallest value of n for which the sampling distribution of p is approximately normal? n = adult Caucasian males

Explanation / Answer

(a)The sample proportion is p=1/190

The mean value of the sample proportion of p^ is: n*p=100*1/190=0.526

The standard deviation is root over p^*(1-p^)/n=root over 1/190*(1-1/190)/100=0.007

(b)The distribution of sample proportion can be approximately normal if np>=10 and np(1-p)>=10

Here, np=100*1/190=0.526 which is less than 10 and np(1-p)=100*1/190*(1-1/190)=0.523 which is also less than 10.

So the answer is (c), No, because np<10.

(c)The smallest value of n should be:

Np=10

Or n*1/190=10

Or n=10*190=1900

For n=1900 the sampling distribution of p^ is approximately normal.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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