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14. Between what symmetrical limits about the true population proportion of 0.08 do (a) 90% of the sample proportions lie (n=64)? (b) 95% of the sample proportions lie (n=64)? (c) 99% of the sample proportions lie (n=64)?.
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14. Between what symmetrical limits about the true population proportion of 0.08 do (a) 90% of the sample proportions lie (n=64)? (b) 95% of the sample proportions lie (n=64)? (c) 99% of the sample proportions lie (n=64)?
(a) 90% of the sample proportions lie (n=64)? = . 08 p = 64 n P(Z < z΄) = 0.5+ .90/2 = .95 = .9500 Z΄ = 1.645 90% Probability P(Z ≤ z’) hundredths Z΄ = 1.645 z’ .04 .05 Z=0 Z units tenths probability in shaded area 1.6 .9495 .9500 .9505
(b) 95% of the sample proportions lie (n=64)? = . 08 p = 64 n P(Z < z΄) = 0.5+ .95/2 = .975 = .9750 Z΄ = 1.96 Z΄ 95% Probability P(Z ≤ z’) hundredths Z΄ = 1.96 z’ .06 Z=0 Z units tenths probability in shaded area 1.9 .9750
(c) 99% of the sample proportions lie (n=64)? = . 08 p = 64 n P(Z < z΄) = 0.5+ .99/2 = .995 = .9950 Z΄ = 2.575 99% Probability P(Z ≤ z’) hundredths Z΄ = 2.575 z’ .07 .08 Z=0 Z units tenths probability in shaded area 2.5 .9949 .9950 .9951