stats 363 HW 8-5

stats 363 HW 8-5 - Section 8.5 Exercise 8.23 The 90...

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Unformatted text preview: Section 8.5 Exercise 8.23 . The 90% con&dence interval for & is given by x & 1 : 645 ¡ p n . ( a ) If n = 125, x = 0 : 84, and s 2 = 0 : 086, then : 084 & 1 : 645 p : 086 p 125 = 0 : 084 & : 043 or : 797 < & < : 883. ( b ) If n = 50, x = 21 : 9, and s 2 = 3 : 44, then 21 : 9 & 1 : 645 p 3 : 44 p 50 = 21 : 9 & : 431 or 21 : 469 < & < 22 : 331. ( c ) Because intervals constructed in this manner will enclose the true value of & about 90% of the time in repeated sampling, it fairly con&dent that these particular intervals will enclose & . Exercise 8.25 . It is given that n = 300 and x = 263. The point estimate of p is given by b p = x n = 263 300 = 0 : 877. Hence, a 90% con&dence interval for p is given by b p & 1 : 645 r pq n ¡ : 877 & 1 : 645 s (0 : 877) (0 : 123) 300 = 0 : 877 & : 031 or : 846 < p < : 908 : Intervals constructed in this manner will enclose the true value of p about 90% of the time in repeated sampling, it fairly con&dent that this particular interval will encloses p .....
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stats 363 HW 8-5 - Section 8.5 Exercise 8.23 The 90...

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