Sampling and Statistics Quiz

What is the primary purpose of sampling in statistics?

• To survey the entire population

• To assume an underlying probability on the population

• To infer the underlying population distribution from sample data

• To assume the sample data are dependent

The sample mean:

• Is a fixed value

• Varies with each sample

• Has the same mean as the population

• Both B and C

The Central Limit Theorem states that for large sample sizes, the distribution of the sample sum will be:

• Uniform

• Skewed

• Normally distributed

• Exponentially distributed

In proportionate sampling, what does the variable represent?

• The total population size

• The number of subsets in the population

• The proportion of the population with a specific characteristic

• The size of each subset

What does sample variance measure in a dataset?

• The average of the data points

• The spread of the data points around the mean

• The sum of the data points

• The product of the data points

What statistical measure decreases with an increase in sample size?

• Mean

• Median

• Mode

• Standard deviation of the sample mean

Which theorem provides the basis for making inferences about population means using the sample mean?

• Bayes' Theorem

• Pythagorean Theorem

• Central Limit Theorem

• Theorem of Total Probability

What is the primary advantage of using stratified sampling over simple random sampling?

• It is simpler to implement

• It reduces the sampling bias

• It increases the variability within subgroups

• It requires a smaller overall sample size

The chi-squared distribution is particularly useful for which type of analysis?

• Predictive modeling

• Time-series analysis

• Goodness-of-fit tests

• Regression analysis

If the sample data are not independent, what assumption of the Central Limit Theorem is violated?

• Distribution assumption

• Independence assumption

• Identically distributed assumption

• Normality assumption