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 41,553 Game of Thrones fans, and found that 8,201 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.

To calculate the required sample size, what value of z* should we use in the formula below to calculate a 90% confidence interval within 3.03 percentage points? Give your answer to 4 decimal places.

n=p*(1−p*)(z*ME)2

Answer 1

Solution :

Given that,

n = 41553

x = 8201

Point estimate = sample proportion = = x / n = 8201 / 41553 = 0.1974

1 - = 1 - 0.1974 = 0.8026

margin of error = E = 0.0303

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.645 / 0.0303 )2 * 0.1974 * 0.8026

= 466.97

sample size = n = 467