Question

2) In 2015, Game of Thrones set a record by winning 12 Emmy awards out of the 24 nominations it received. The 50 episodes show so far have averaged almost exactly 5 million viewers per episode, with a standard deviation of 1.78. Assume that this is a sample of 50 taken from a larger distribution, and make a 94% confidence interval for the true population mean. What is the lower limit of the interval? (Note: solve the problem using 5 & 1.78, ignoring the word "million.")

Answer 1

It is given that

= 5 (sample mean)

sample size n= 50

= 1.78 (we considered it sigma because sample size is large enought to assume it normally distributed)

z score for 94% confidence interval using the z distribution table 1.88

Formula for lower limit of confidence interval is given as

CI = - z*(/sqrt{n}) {sqrt means square root of n}

putting this values

= 5 - [1.88*(1.78/sqrt{50})]

= 5 - [1.88*0.2517]

= 5 -0.4733 = 4.5267

Lower limit = 4.5267 (rounded 4 decimals) or 4.53 (rounded to 2 decimals) or 4.527(rounded to 3 decimals)