Question

Game of Thrones ~ The creators David Benioff and D. B. Weiss of the TV show “Game of Thrones”, want to know how popular Season 8 was among the show’s fans. They hired an analyst who collected a random sample of 41035 Game of Thrones fans, and found that 8243 of those fans said that they like Season 8. Using this data, the analyst wants to estimate the actual proportion of fans who like Season 8.

We want to use statistical inference to estimate the actual proportion of fans who like Season 8.

To use a normal distribution in this scenario, which of the following conditions must be satisfied?

Question 5 options:

	Both n×p0 and n×(1−p0)} is the null value for the population proportion.
	The observations within the sample must be independent of each other.
	There must be at least 10 observed successes and 10 observed failures in the sample.
	Any two samples must be independent of each other.

Answer 1

The test procedure, for one sample z-test, is appropriate to use a normal distribution when the following conditions are met:

• The sampling method for the population is simple random sampling also
• The samples are independent.
• Each sample includes at least 10 successes and 10 failures.

Thus, using the above statement the conditions that must be satisfied for using normal distribution are:

i) The observations within the sample must be independent of each other.

ii) There must be at least 10 observed successes and 10 observed failures in the sample.

iii) Any two samples must be independent of each other.