Question

(10 points) The 2010 General Social Survey asked 1225 US residents: "Do you think the use of marijuana should be made legal, or not? Of the respondents, 600 said it should be made legal. 1. The value 48.98% is a... A. population parameter B. sample statistic 2. Construct a 95% confidence interval for the proportion of US residents who think marijuana should be made legal, and interpret it in the context of the data. Round your results to four decimal places. 3. Identify each of the statements below as TRUE or FALSE. ? 1. There is a 95% chance that the proportion of US residents who think marijuana should be made legal falls within the interval computed in part 2. ? 2. The opinion of marijuana legalization of 95% of US residents falls within the interval computed in part 2. ? 3. We are 95% confident that the true proportion of US residents who think marijuana should be made legal falls within the interval computed in part 2. ? 4. If we repeated this study many times, we would expect approximately 95% of future intervals to contain the true proportion of US residents who think marijuana should be made legal. ? 5. If we repeated this study many times, we would expect the sample proportion of US residents who think marijuana should be made legal to fall within the interval computed in part 2 approximately 95% of the time. 4. A critic points out that this 95% confidence interval is only accurate if the statistic follows a normal distribution, or if the normal model is a good approximation. Is this true for these data? ? , because ?

Answer 1

1)

B. sample statistic

(since it is based on sample of 1225)

2(

sample success x =		600
sample size          n=		1225
sample proportion p̂ =x/n=		0.4898
std error se= √(p*(1-p)/n) =		0.0143
for 95 % CI value of z=		1.960
margin of error E=z*std error   =		0.0280
lower bound=p̂ -E                       =		0.4618
Upper bound=p̂ +E                     =		0.5178

95% confidence interval =(0.4618 , 0.5178)

3. Identify each of the statements below as TRUE or FALSE. ?False 1. There is a 95% chance that the proportion of US residents who think marijuana should be made legal falls within the interval computed in part 2. ? False 2. The opinion of marijuana legalization of 95% of US residents falls within the interval computed in part 2. True - 3. We are 95% confident that the true proportion of US residents who think marijuana should be made legal falls within the interval computed in part 2. ?True 4. If we repeated this study many times, we would expect approximately 95% of future intervals to contain the true proportion of US residents who think marijuana should be made legal. False 5. If we repeated this study many times, we would expect the sample proportion of US residents who think marijuana should be made legal to fall within the interval computed in part 2 approximately 95% of the time. 4. A critic points out that this 95% confidence interval is only accurate if the statistic follows a normal distribution, or if the normal model is a good approximation. Is this true for these data? Yes, because ? np and n(1-p) both are greater than 10