#1
What is sampling in statistics?
The process of selecting a subset of individuals from a population
The process of calculating the mean of a dataset
The process of visualizing data using graphs
The process of analyzing categorical data
#2
What is the purpose of statistical inference?
To describe and summarize data
To make predictions or inferences about a population based on sample data
To organize data in tables and charts
To measure the variability of data
#3
What is the purpose of a hypothesis test in statistics?
To estimate the population parameters with a high level of precision
To determine if there is a significant difference between two or more groups
To summarize the data using descriptive statistics
To visualize the data using graphs and charts
#4
Which of the following is NOT a measure of central tendency?
#5
Which of the following sampling methods is based on random selection and ensures each member of the population has an equal chance of being chosen?
Stratified sampling
Systematic sampling
Cluster sampling
Simple random sampling
#6
What is the standard error of the mean?
The standard deviation of the population
The average of the sample data
The standard deviation of the sampling distribution of the sample mean
The margin of error in hypothesis testing
#7
What is the purpose of a confidence interval in statistics?
To determine the statistical power of a hypothesis test
To estimate the range within which the population parameter is likely to fall
To calculate the probability of a Type I error
To assess the normality of the data distribution
#8
Which of the following is NOT a requirement for conducting a hypothesis test?
Random sampling
Normal distribution of data
Independent observations
Equal variances of samples
#9
Which statistical test is appropriate for comparing the means of two independent groups?
Paired t-test
Chi-square test
Independent samples t-test
ANOVA test
#10
What is stratified sampling?
A sampling method where the population is divided into groups and a random sample is taken from each group
A sampling method where the population is divided into clusters and a random sample of clusters is chosen
A sampling method where every nth individual is selected from a list of the population
A sampling method where individuals are selected based on convenience
#11
Which of the following statements is true about Type I error?
Type I error occurs when the null hypothesis is incorrectly rejected
Type I error occurs when the null hypothesis is incorrectly accepted
Type I error occurs when the alternative hypothesis is incorrectly accepted
Type I error occurs when the alternative hypothesis is incorrectly rejected
#12
In statistical inference, what does a p-value represent?
The probability of rejecting the null hypothesis when it is true
The probability of failing to reject the null hypothesis when it is false
The probability of accepting the alternative hypothesis
The probability of observing the sample data or more extreme data, given that the null hypothesis is true
#13
Which of the following statements about Type I and Type II errors is correct?
Type I error occurs when the null hypothesis is incorrectly rejected
Type II error occurs when the null hypothesis is correctly rejected
Type I error is also known as the power of the test
Type II error is the probability of correctly accepting the null hypothesis
#14
What is the central limit theorem?
A theorem stating that the mean of a sufficiently large sample follows a normal distribution, regardless of the population distribution
A theorem stating that the standard deviation of a population decreases as the sample size increases
A theorem stating that the median of a sample is equal to the median of the population
A theorem stating that the sample mean is always equal to the population mean
#15
What is the formula for calculating the margin of error in a confidence interval?
z * (standard deviation / square root of sample size)
t * (standard deviation / square root of sample size)
z * (standard deviation / sample size)
t * (standard deviation / sample size)
#16
What is the formula for the standard error of the mean (SEM)?
Standard deviation / square root of sample size
Square root of sample size / standard deviation
Standard deviation * square root of sample size
Sample size / standard deviation
#17
Which of the following statements about the t-distribution is correct?
The t-distribution is symmetric and bell-shaped
The t-distribution has fatter tails than the standard normal distribution
The t-distribution has a mean of 1 and a standard deviation of 1
The t-distribution is used when the sample size is large
#18
What is the purpose of a Type II error in hypothesis testing?
To incorrectly reject the null hypothesis when it is true
To incorrectly fail to reject the null hypothesis when it is false
To correctly reject the null hypothesis when it is true
To correctly fail to reject the null hypothesis when it is false