Chapter 6, Section 7, Exercise 163 Male-Female Ratios Of the 50 states in the Un
ID: 3042889 • Letter: C
Question
Chapter 6, Section 7, Exercise 163 Male-Female Ratios Of the 50 states in the Unites States, Alaska has the largest percentage of males and Rhode Island has the largest percentage of females. (Interestingly, Alaska is the largest state and Rhode Island is the smallest). According to the 2010 US Census, the population of Alaska is 52.0 % male and the population of Rhode Island is 48.3 % male. If we randomly sample 340 people from Alaska and 350 people from Rhode Island, what are the mean and standard error of p Overscript ^ EndScripts Subscript a Baseline minus p Overscript ^ EndScripts Subscript StartItalic ri EndItalic, where p Overscript ^ EndScripts Subscript a is the proportion of males in the Alaskan sample and p Overscript ^ EndScripts Subscript StartItalic ri EndItalic is the proportion of males in the Rhode Island sample? Round your answers to three decimal places.
Explanation / Answer
Pooled sample proportion P = (p1 * n1 + p2 * n2)/(n1 + n2)
= (0.52 * 340 + 0.483 * 350)/(340 + 350) = 0.5
Standard error (SE) = sqrt (P * (1 - P) * (1/n1 + 1/n2))
= Sqrt (0.5 * 0.5 * (1/340 + 1/350))
= 0.038
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