Respuesta :
Answer:
a) MOE = 0.0190
b) MOE = 0.0245
c) No, because the margin of error depends on the standard error, and the later depends on the proportion. The closer the proportion to 0.5, the larger the standard error (for equal sample size).
Step-by-step explanation:
The question is incomplete:
Fewer young people are driving. In 1983, 87% of 19-year-olds had a driver's license. Twenty-five years later that percentage had dropped to 75% (University of Michigan Transportation Research Institute website, April 7, 2012). Suppose these results are based on a random sample of 1200 19-year-olds in 1983 and again in 2008.
a) The sample proportion is p=0.87.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.87*0.13}{1200}}\\\\\\ \sigma_p=\sqrt{0.000094}=0.0097[/tex]
The critical z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.0097=0.019[/tex]
b) The sample proportion is p=0.75.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.75*0.25}{1200}}\\\\\\ \sigma_p=\sqrt{0.000156}=0.0125[/tex]
The critical z-value for a 95% confidence interval is, as in point a, z=1.96.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.0125=0.0245[/tex]
c) No, because the margin of error depends on the standard error, and the later depends on the proportion. The closer the proportion to 0.5, the larger the standard error (for equal sample size).
