#1
Which of the following is a point estimator for the population mean?
Sample mean
ExplanationA single value used to estimate the population mean.
#2
What is the relationship between sample size and the margin of error in a confidence interval?
Inverse relationship: as sample size increases, margin of error decreases
ExplanationAs the sample size increases, the estimate becomes more precise.
#3
In statistical hypothesis testing, what does the null hypothesis usually state?
The absence of an effect or difference
ExplanationAssumes no relationship or no difference.
#4
What is the formula for calculating the coefficient of variation (CV)?
(Sample standard deviation / Sample mean) * 100
ExplanationMeasures the relative variability of a dataset.
#5
What is the standard error of the sample mean?
Sample variance divided by sample size
ExplanationThe standard deviation of the sampling distribution of the sample mean.
#6
In hypothesis testing, what is the p-value?
The probability of observing a sample statistic as extreme as, or more extreme than, the one observed
ExplanationProbability of obtaining results at least as extreme as the observed results, assuming the null hypothesis is true.
#7
What is the purpose of the Central Limit Theorem in statistics?
To describe the distribution of a sample mean, regardless of the original population distribution
ExplanationStates that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.
#8
What does the term 'statistical power' refer to in hypothesis testing?
The likelihood of correctly rejecting a false null hypothesis
ExplanationProbability of detecting an effect, given that the effect truly exists.
#9
What is the purpose of a Type I error in hypothesis testing?
To incorrectly accept a false null hypothesis
ExplanationRejecting the null hypothesis when it is actually true.
#10
What is the formula for the confidence interval of the population mean?
Sample mean ± t* × (Sample standard deviation / √sample size)
ExplanationA range of values within which the true population mean is likely to lie.
#11
What is the purpose of bootstrapping in statistical inference?
To estimate the sampling distribution of a statistic by resampling with replacement from the observed data
ExplanationEstimating the variability of a statistic by sampling with replacement from the observed data.
#12
In regression analysis, what does the coefficient of determination (R-squared) represent?
The proportion of the dependent variable explained by the independent variable
ExplanationPercentage of the response variable variation explained by the regression model.
#13
What is the purpose of the standard normal distribution (Z-distribution) in statistical analysis?
To standardize normal distributions with different means and standard deviations
ExplanationAllows comparison of values from different normal distributions.
#14
What is the formula for calculating the margin of error in a confidence interval?
t* × (Sample standard deviation / √sample size)
ExplanationMeasures the accuracy of the estimate.