Question

A researcher wishes to estimate, with 99% confidence, the population proportion of adults who support labeling legislation for genetically modified organisms (GMOs). Her estimate must be accurate within 6% of the true proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 83% of the respondents said they support labeling legislation for GMOs. (c) Compare the results from parts (a) and (b).

Answer 1

(a)

Proportion = p = 0.5 Margin of Error = E = 0.06 Confidence Level = 99 Significance Level = Q = (100-99)% = 0.01 a/2 = (0.01/2) = 0.005 Critical Value = z* = 2.576 [using Excel NORM.S.INV(0.005)] Sample size = n = p(1-P) = 0.5*(1-0.5)*(2.576/0.06)2 = 460.76 ~ 461 (ans) E

(b)

Proportion = p = 0.83 Margin of Error = E = 0.06 Confidence Level = 99 Significance Level = a = (100-99)% = 0.01 a/2 = (0.01/2) = 0.005 Critical Value = z* = 2.576 [using Excel NORM.S.INV(0.005)] Sample size = n = p(1-p) = 0.83*(1-0.83)*(2.576/0.06)2 = 260.05 > 261 (ans) E

(c) Having prior study, decreases the sample size.