Question

Assume you have a population of 30000 people where 5% of the population has some particular disease.

List the given numeric information along with the correct symbols.

? = 30000

? = 5%

a) If you take a sample of size 58, can we say that the sampling distribution of ˆ p is approximately normal? Why or why not?

Check conditions:

1. np = which (symbol) ____________

2. n(1 - p) = which ? (symbol) ___________

3. and N = which ? (symbol) ____________

Can we say that the sampling distribution of ˆ p is approximately normal in this case?

(If the answer is no, state the first conditions in the list above that failed)

b) Redo part a assuming p has increased to 89%. Check conditions:

1. np = which ? (symbol) ____________

2. n(1 - p) = which ? (symbol) ______________

3. and N = which ? (symbol) ________________

Can we say that the sampling distribution of ˆ p is approximately normal in this case?

(If the answer is no, state the first conditions in the list above that failed)

c) If you take a sample of size 595 from the original population where p is 5%, can we say that the sampling distribution of ˆ p is approximately normal? Why or why not?

Check conditions:

1. np = which ? (symbol) ______________

2. n(1 - p) = which ? (symbol) ____________

3. and N = which ? (symbol) ______________

Can we say that the sampling distribution of ˆ p is approximately normal in this case?

(If the answer is no, state the first conditions in the list above that failed)

d) Redo part c assuming the population only has 10098 people in it. Check conditions:

1. np = which ? (symbol) ___________

2. n(1 - p) = which ? (symbol) ________________

3. and N = which ? (symbol) ___________

Can we say that the sampling distribution of ˆ p is approximately normal in this case? (If the answer is no, state the first conditions in the list above that failed)

e) In the last section a sample size of at least 30 was large enough to use the normal distribution to compute probabilities. How are the problems in this section different?

Answer 1

N = 30000

p = 5%

a) 1. np = 2.9 < 5

2. n(1 - p) = 55.1 5

3. and N = 30000

No, since the first condition did not check out.

b) 1. np = 51.62 5

2. n(1 - p) = 6.38 5

3. and N = 30000

Yes

c) 1. np = 29.75 5

2. n(1 - p) = 565.25 5

3. and N = 30000

Yes

d) 1. np = 29.75 5

2. n(1 - p) = 565.25 5

3. and N = 10098

Yes