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 2% 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 81% of the respondents said they support labeling legislation for GMOs, (c) Compare the results from parts (a) and (b) (a) What is the minimum sample size needed assuming that no prior information is available? n- 4161 (Round up to the nearest whole number as nooded) (b) What is the minimum sample size needed using a prior study that found that 81% of the respondents support labeling legislation? (Round up to the nearest whole number as nooded.) 12

Answer 1

( b )

The following information has been provided a = 0.01, E = 0.02 The provided estimate population proportion pis p = 0.81. The critical value for the significance level a = 0.01 is ze = 2.58. The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error 2.58 n2p(1-P) () * = 0,81(1 - 0.81) 2552.78 0.02 Therefore, the sample size needed to satisfy the condition n 2552.78, and it must be an integer number, we conclude that the minimum required sample size is n = 2553.

Answer : n = 2553

( c )

having an estimate of the population proportion reduces the minimum sample size needed