Answer:
Step-by-step explanation:
a) Sample statistics are used to estimate population value. Since 48% is a sample proportion, therefore, it is a sample statistic.
b) For 95% confidence level, z* = 1.96.
\hat{p}\pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}= 0.61\pm 0.61\sqrt{\frac{0.61(1-0.61)}{1578}}=0.61\pm 0.024 \ or (0.586, 0.634).
We are 95% confident that the true proportion of US residents who think marijuana should be made legal lies between 58.6% and 63.4%.
c)
\\np=1578(0.61)=962.58
\\n(1-p)=1578(1-0.61)=615.42
Since both np and n(1-p), are at least 10, the normal model is a good approximation for these data.
d) As the lower limit of confidence interval is less than 0.5, less than 50% population is also a plausible value of true proportion. This means the statement "Majority of Americans think marijuana should be legalized" is not justified.
