Question

A survey asked, "How many tattoos do you currently have on your body?" Of the 1215 males surveyed, 182 responded that they had at least one tattoo. Of the 1033 females surveyed, 135 responded that they had at least one tattoo. Construct a 90% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval. Let pa represent the proportion of males with tattoos and P2 represent the proportion of females with tattoos. Find the 90% confidence interval for P1-P2. The lower bound is The upper bound is (Round to three decimal places as needed.) Interpret the interval. O A. There is 90% confidence that the difference of the proportions is in the interval. Conclude that there is a significant difference in the proportion of males and females that have at least one tattoo.
I need help with the first two please and Is the last one correct?

Answer 1

Given that = ni For population 1 (males): X1 182 and ni - 1215. 182 P1 = 1215 For population 2 (females): x2 = 135 and n2 = 1033. 135 P2 1033 12 a) Now we have to find the 90% confidence interval for difference in proportion (P1-P2). Step (1): 90 1- = 1-0.90 = 0.10 100 0.10 0.05 2

Step (2): Required probability = 1-0.05 = 0.95 End the value of z such that P(Z < z) = 0.95 From standard normal table z = 1.645 (Or) Use excel formula: ENORM.S.INV(0.95) Step (3): 182 135 P1 - P2 = 0.019 1215 1033 pooled proportion p = x1+xz n1+12 182+135 1215+1033 0.1410 =z* fp(1-P) Car + Margin of error E Þ(1 – P) (+ ) = 0.024 Step (4): Lower bound = (P1-P2) - (E) = 0.019 -0.024 = -0.005 Upper bound= (P1-P2) + (E) = 0.019 + 0.024 = 0.043 .. Lower bound = -0.005 Upper bound = 0.043

b) Now we have to write the interpretation. Interpretation: Our 90% confidence interval does included 'O' value. There is insufficient evidence. :: Option(B) is the answer.

thank you