Question

A Normal model states that if we draw repeated random samples of the same​ size, n, from some population and measure sample​ proportions, then the collection of these proportions will pile up around the underlying population​ proportion, p. The requirement for this to work is​ _______.

Answer 1

Answer:

1) Randomization condition: We assume that we are selecting random samples so this condition is satisfied

2) 10% condition: We assume that the random sample selected is less than 10% of the population size

3) Success/ Failure condition:

For this case we need to satisfy this:

$np \geq 10, n(1-p)\geq 10$

So since the condition 1 and 2 are satisfied the correct option for this case would be:

a)np and nq must be respectively at least equal to 10

Step-by-step explanation:

Assuming the following options:

a)np and nq must be respectively at least equal to 10

b) as n increases, the distribution of sample proportions becomes less Normal

c) np and nq must be respectively less than 10

d) np plus nq must be at least 10.

For this case we need 3 basic conditions:

1) Randomization condition: We assume that we are selecting random samples so this condition is satisfied

2) 10% condition: We assume that the random sample selected is less than 10% of the population size

3) Success/ Failure condition:

For this case we need to satisfy this:

$np \geq 10, n(1-p)\geq 10$

So since the condition 1 and 2 are satisfied the correct option for this case would be:

a)np and nq must be respectively at least equal to 10