Question

Harry Potter ~ Many people love reading books like Harry Potter. Historically, it has been estimated that the proportion of book readers, who like to read fiction, is 0.6. Camille is a Harry Potter fan and a fan of fiction books.

She wants to determine if the actual proportion of book readers who like to read fiction is different from the historical value. From a recent survey of randomly selected 15000 book readers, she learns that 7000 like to read fiction.
To use a normal distribution in this scenario, which of the following conditions must be satisfied?

Question 6 options:

	There must be at least 10 observed successes and 10 observed failures in the sample.
	Both n×p0 must be at least 10 where p0 is the null value for the population proportion.
	Any two samples must be independent of each other.
	The observations within the sample must be independent of each other.

Answer 1

Answer:

Here to use the normal distribution, there is a condition to be satisfied

i.e.,

(i) The sample size must be large.

(ii) np & nq >= 10

i.e.,

n(1-po) >= 10

n - npo >= 10

n >= 10 + npo

n >= 20

So Option B is right choice.

i.e.,

Both n×p0 must be at least 10 where p0 is the null value for the population proportion.