Question

1. Across all 8 seasons of Game of Thrones, female speech amounts to only about 25% of all speaking time. Assume there were about 5703 minutes of speaking time across all 8 seasons of Game of Thrones. a. Find and interpret a 90% level confidence interval for p, the true proportion of speaking time for females in Game of Thrones. b. In season 8 episode 4, only 20% of all speaking time was attributed to female characters. Based on your interval in part (a), was this value likely? c. If we wanted to be 95% certain that a confidence interval for the true proportion of female speech had a margin of error of no more than 1%, how many minutes of speaking time would we need to have in our sample? Use P = 0.25.

Answer 1

P= proportion of female speech = 0.25 of all speaking time n = total minutes of speaking time - 5703 (a) bet ļ be true proportion of speaking time to females in GOT Given, 2 = 100-90=10% - 1-2/2 = 50% -) 2 (0.95) = 1.64 90.). (I Er p is (& r fe (1-6] +Z1095) (0.25 I 0.25 0.75 * 1.64 - (0.25 I 0.0094) = (0.2406, 0. 2594) . Im all possible samples, the true proportion ? lies blw (0.2406, 0.2594) in 90% of the samples (b) Ho: P = 0.2 Hi P70.2 since 0.2 (I =) We reject Ho doesn't belongs to above =) P=0.2 is not likely (c) d=5% = 1-2/2 = 0.975 =) Z(0.975)=1.96 5703 Margin of erros a 0.01 n 0.01 - 260.975). § (1-13 <0-0) =) 1.96* [ 0.25 +0.75 <0.01 =) In > 1964J0.25 +0.75 - in - 84-87 =) no 7202.9 At least 7203 minutes of speaking time -