Question

Vermont Lawmakers in the year 2021 are interested in how the law that increased the legal age to buy to vaping products has changed the proportion of young adults who use these products. Back in 2019, the Pew Research group found that 2 in 10 people age 18-29 regularly use these products.

Using that prior estimate as they plan for the upcoming survey, how many people would need to be sampled to be within 2.46 % of the true proportion of people who use these products at the 95% level of confidence? Round up.

Answer 1

Solution :

Given that,

= x/n=2/10=0.2

1 - = 1 - 0.2 = 0.8

margin of error = E = 2.46% = 0.0246

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96 / 0.0246)2 * 0.2 * 0.8

= 1015.69

Sample size =1016