Question

The 2010 General Social Survey asked 1,259 US residents: "Do you think the use of marijuana should be made legal, or not?" 48% of the respondents said it should be made legal.

1. The value 48% 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 3 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 that approved of legalization falls within the interval computed in part 2.

? True False  2. The approval rating of 95% of US residents falls within the interval computed in part 2.

? True False  3. We are 95% confident that the true approval rate of US residents falls within the interval computed in part 2.

? True False  4. If we repeated this study many times, we would expect 95% of future intervals to contain the true approval rating of US residents.

? True False  5. If we repeated this study many times, we would expect the population proportion who approve of marijuana to fall within the interval computed in part 2 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 1,259 is not large enough for the central limit theorem to apply .

5. A news piece on this survey's findings states, Majority of Americans think marijuana should be legalized.'' Based on your confidence interval, is this news piece's statement justified?

? Yes No , because  ? the confidence interval includes reasonable values for the parameter that are below 50% we did not conduct a hypothesis test the confidence interval includes reasonable values for the parameter that are above 50% this is an observational study and not an experiment .

Answer 1

1.

Here 48% is the Proportion of Residents who wants the legalization of marijuana use

so

B. population parameter

2.

we have sample size =n=1259

P=0.48

so

95% confidence interval is given by

So Interval is (0.452,0.508)

3.

  1. There is a 95% chance that the proportion of US residents that approved of legalization falls within the interval computed in part 2. False

  2. The approval rating of 95% of US residents falls within the interval computed in part 2. False

  3. We are 95% confident that the true approval rate of US residents falls within the interval computed in part 2. False

4. If we repeated this study many times, we would expect 95% of future intervals to contain the true approval rating of US residents. True

  5. If we repeated this study many times, we would expect the population proportion who approve of marijuana to fall within the interval computed in part 2 95% of the time.False

4.

Yes ,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 1,259 is large enough for the central limit theorem to apply .

5.

Yes because the confidence interval includes reasonable values for the parameter that  are above 50% this is an observational study and not an experiment