#1
What is statistical inference?
The process of making predictions about a population based on sample data
ExplanationPredicting population characteristics from sample data.
#2
What is a population proportion?
The ratio of a specific subset to the total population
ExplanationRatio of a subset to the whole population.
#3
What is the formula to calculate the margin of error for a population proportion?
(z * √(p̂(1-p̂))/n)
ExplanationFormula for calculating margin of error.
#4
In a survey of 500 people, 70% prefer option A. What is the point estimate for the population proportion?
0.7
ExplanationPoint estimate equals sample proportion.
#5
What is the confidence level in statistical inference?
The probability that the sample statistic falls within a certain range of the population parameter
ExplanationProbability that sample statistic reflects population parameter.
#6
What is the purpose of a hypothesis test for population proportions?
To determine if the sample proportion is statistically significant
ExplanationTesting if sample proportion is significant.
#7
What is the standard error of the sample proportion?
The standard deviation of the sample proportion
ExplanationStandard deviation of sample proportion.
#8
In hypothesis testing for population proportions, what is the null hypothesis?
There is no difference between the sample proportion and the population proportion
ExplanationNull hypothesis assumes no difference between sample and population proportions.
#9
What is the formula to calculate the sample size required for estimating a population proportion with a desired margin of error?
(z^2 * p̂(1-p̂)) / (E^2)
ExplanationFormula to determine sample size.
#10
What assumption is typically made when constructing a confidence interval for a population proportion?
The population distribution is normally distributed
ExplanationAssumption of normal distribution.
#11
What is Type I error in hypothesis testing for population proportions?
Rejecting the null hypothesis when it is true
ExplanationIncorrectly rejecting a true null hypothesis.
#12
What is Type II error in hypothesis testing for population proportions?
Failing to reject the null hypothesis when it is false
ExplanationIncorrectly retaining a false null hypothesis.