Answer:
a) Statistic.
b) The population proportion is expected to be between 0.29 and 0.31 with a 94% degree of confidence.
Step-by-step explanation:
a) The proportion of 30% is a statistic, as it is a value that summarizes data only from the sample taken in the study from USA Today. Other samples may yield different proportions.
b) We can use the statistic to estimate a confidence interval for the parameter of the population.
The standard error for the proportion is calculated as:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{N}}=\sqrt{\dfrac{0.3\cdot 0.7}{7335}}=\sqrt{2.83\cdot10^5}= 0.00535[/tex]
The margin of error is 0.01. We can use this value to determine the level of confidence that represents.
The formula for the margin of error is:
[tex]E=z\cdot \sigma_p=0.01\\\\z\cdot 0.0535=0.01\\\\z=1.87[/tex]
This z-value, according to the the standard normal distribution, corresponds to a confidence interval of 94%.
The interval for this margin of error is:
[tex]p-E\leq \pi \leq p+E\\\\0.30-0.01\leq \pi \leq 0.30+0.01\\\\0.29\leq \pi \leq 0.31[/tex]
Then, we can conclude that the population proportion is expected to be between 0.29 and 0.31 with a 94% degree of confidence.
