In: Statistics and Probability
A researcher wishes to estimate, with 90% confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 4% 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 32% of the respondents said they think their president can control the price of gasoline. c) Compare the results from parts (a) and (b). (a) What is the minimum sample size needed assuming that no prior information is available? nequals nothing (Round up to the nearest whole number as needed.)
Solution :
Given that,
margin of error = E = 0.04
At 90% confidence level the z is ,
= 1 - 90% = 1 - 0.90 = 0.10
/ 2 = 0.10 / 2 = 0.05
Z/2 = Z0.05 = 1.645
(a)
= 0.5
1 - = 1 - 0.5 = 0.5
sample size = n = (Z / 2 / E )2 * * (1 - )
= (1.645 / 0.04)2 * 0.5 * 0.5
= 422.81 = 423
sample size = 423
(b)
= 0.32
1 - = 1 - 0.32 = 0.68
sample size = n = (Z / 2 / E )2 * * (1 - )
= (1.645 / 0.04)2 * 0.32 * 0.68
= 368.01
sample size = 368
c)
Having an estimate of the population proportion reduces the minimum sample size is needed .