stats 363 HW 7-6

# stats 363 HW 7-6 - Section 7.6 Exercise 7.37 The mean and...

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Section 7.6 Exercise 7.37 . The mean and standard deviation of the sampling distrib- ution of the sample proportion b p are, respectively, given by E ( b p ) = p and SE ( b p ) = r pq n : ( a ) If n = 100 and p = 0 : 3, then E ( b p ) = 0 : 3 and SE ( b p ) = s (0 : 3) (0 : 7) 100 = 0 : 0458 : ( b ) If n = 400 and p = 0 : 1, then E ( b p ) = 0 : 1 and SE ( b p ) = s (0 : 1) (0 : 9) 400 = 0 : 015 : ( c ) If n = 250 and p = 0 : 6, then E ( b p ) = 0 : 6 and SE ( b p ) = s (0 : 6) (0 : 4) 250 = 0 : 0310 : Exercise 7.41 . The standard deviation of the sampling distribution of the sample proportion b p is given by SE ( b p ) = r pq n : Assume that n = 100. ( a ) If p = 0 : 01, then SE ( b p ) = s (0 : 01) (0 : 99) 100 = 0 : 0099 : ( b ) If p = 0 : 10, then SE ( b p ) = s (0 : 10) (0 : 90) 100 = 0 : 03 : ( c ) If p = 0 : 30, then SE ( b p ) = s (0 : 30) (0 : 70) 100 = 0 : 0458 : ( d ) If p = 0 : 50, then SE ( b p ) = s (0 : 5) (0 : 5) 100 = 0 : 05 :

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( e ) If p = 0 : 70, then SE ( b p ) = s (0 : 70) (0 : 30) 100 = 0 : 0458 : ( f ) If p = 0 : 90, then SE ( b p ) = s (0 : 90) (0 : 10) 100 = 0 : 03 : ( g ) If p = 0 : 99, then SE ( b p ) = s (0 : 99) (0 : 01) 100 = 0 : 0099 : Exercise 7.43 . Let p denote the population proportion of Americans who relieve stress by overeating sweet foods. Assume that p = 46% and a random sample of n = 100 Americans is selected.
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