- In a 2010 Survey USA poll, 70% of the 119 respondents between the ages of 18 and 34 said they would vote in the 2010 general election for Prop 19, which would change California law to legalize marijuana and allow it to be regulated and taxed. At a 95% confidence level, this sample has an 8% margin of error. Based on this information, determine if the following statements are true or false, and explain your reasoning.
November 14, 2018
6.5 Prop 19 in California
We are 95% confident that between 62% and 78% of the California voters in this sample support Prop 19.
- A confidence interval is meant to estimate the population proportion, not the sample proportion.
- So FALSE
- But technically we're 100% sure the sample proportion is 70%, so a lawyer…
We are 95% confident that between 62% and 78% of all California voters between the ages of 18 and 34 support Prop 19.
- Yes, the confidence interval tells us there's a 19 of 20 chance that the true population proportion (18-34 CA) that supports marijuana legalization is 70% +/- 8%.
- TRUE
If we considered many random samples of 119 California voters between the ages of 18 and 34, and we calculated 95% confidence intervals for each, 95% of them will include the true population proportion of 18-34 year old Californians who support Prop 19.
- Yes, TRUE
- This is the essence of what a confidence interval is.
In order to decrease the margin of error to 4%, we would need to quadruple (multiply by 4) the sample size.
- Margin of error formula:
- So to go from 8% to 4%, need to increase the sample size 2^2, or 4.
Based on this confidence interval, there is sufficient evidence to conclude that a majority of California voters between the ages of 18 and 34 support Prop 19.
- TRUE
- The lower end of our 95% CI is 62%, so it is very reasonable to conclude that a majority of our population of voters (CA 18-34) support Prop 19.