Question

Question 11 (8 points) (6 points) A sample of 100 stage actors found 64 were extroverts. Another sample of 94 movie actors found 48 were extroverts. Find a 95% confidence interval for the difference p1 - p2 between the true proportions of stage and movie actors who are extroverts. (2 points) Based on this interval, can we say with 95% confidence that the proportions of stage and movie actors who are extroverts are different?

Answer 1

Question ili Solution: The provided information is, - Sample size Ilog = 100 number of favorable cases (x1= 64 .. sample size 2 (62) 94 numbers of favorable cases 2 (rei) = 48. confidence Level Ingz0ias - The Sample proporties. I is computed as followss 2 X 1264 .64 in Joop - The sample proportion 2 is computed as followers .. pa. X2 = 48 = 0.51 . The fmitical value for go 0.05 is zco Isole = 1.96. The comesponding confidence. Po temal computed as - Shown below CI= ( pi-pê - 2c | A Copa p (15p23 inana, h - p²t. 2. pClopi + p2 (1-2) vni (0.69-0.511 -1.96x10,64(1-0.69) +0.51 Croisin v 100- 94 0.64 -0,5141.96x 0.64(1-0,64) + 0. sij(1 sil).) 100 Ct = (-0.009, 0,267)

Therefore as% confidence internal for the difference pl-p2 between the the proportions of stage and maie actors wloo are extroverats is's cial-Qoog, 0.2672 Bertone i We know that if the confidence internal for the differences does not contain zero, we can conclude that there is a statistically significant difference in the two population votues at the given level of confidence. Here our internal contains zero, so we can conclude that there is not statistica My significant difference in the two population propostes Therefore we can say with 95% confidence that the propostions of stage and movie actors who are extroversts are not different.