Question

6.5 Prop 19 in California: 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.

(a) We are 95% condent that between 62% and 78% of the California voters in this sample support Prop 19.

1. false

2. true

b) We are 95% condent that between 62% and 78% of all California voters between the ages of 18 and 34 support Prop 19.

1. false

2. true

(c) 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.

1. false

2. true

(d) In order to decrease the margin of error to 4%, we would need to quadruple (multiply by 4) the sample size.

1. false

2. true

(e) 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.

1. false

2. true

Answer 1

(a) We are 95% condent that between 62% and 78% of the California voters in this sample support Prop 19.

1. false

b) We are 95% condent that between 62% and 78% of all California voters between the ages of 18 and 34 support Prop 19.

2. true

(c) 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.

1. false

(d) In order to decrease the margin of error to 4%, we would need to quadruple (multiply by 4) the sample size.

2. true

(e) 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.

2. true

Please let me know in case of any doubt.

Thanks in advance!

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