Question

The 2010 General Social Survey asked 1208 US residents: "Do you think the use of marijuana should be made legal, or not?" Of the respondents, 585 said it should be made legal.

1. The value 48.43% is a...

A. sample statistic
B. population parameter

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.

? True 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.

? True False  2. The opinion of marijuana legalization of 95% of US residents falls within the interval computed in part 2.

? True False  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 False  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.

? True 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 No , because  ? there are at least 10 successes and 10 failures in the sample there are at least 20 combined successes and failures in the sample the population has more than 10 successes and 10 failures the sample of 1208 is not large enough for the central limit theorem to apply .

Answer 1

1. The value 48.43% is a : A. sample statistic

2)

sample success x =		585
sample size          n=		1208
sample proportion p̂ =x/n=		0.4843
std error se= √(p*(1-p)/n) =		0.0144
for 95 % CI value of z=		1.960
margin of error E=z*std error   =		0.0282
lower bound=p̂ -E                       =		0.4561
Upper bound=p̂ +E                     =		0.5125

from above 95% confidence interval for population proportion =(0.4561 ,0.5125)

3)

1) false

2) false

3) true

4) true

5) false

4)

yes because there are at least 10 successes and 10 failures in the sample