Statistics and Probability Quiz 11

In probability sampling, what does every member of the population have?

• An equal chance of being selected

• No chance of being selected

• A random chance of being selected

• A higher chance of being selected

Which sampling method involves selecting every nth individual from a population?

• Cluster sampling

• Systematic sampling

• Simple random sampling

• Stratified sampling

A small sample(n<30) is taken from a normal distribution with an unknown variance. Which distribution should be used to find the confidence interval of the mean.

• Normal Distribution

• Z-distribution

• t-distribution

• Chi-squared

Which of the following is a type of non-probability sampling?

• Stratified sampling

• Simple random sampling

• Convenience sampling

• Systematic sampling

What is the term for the process of selecting a section of the population?

• Sampling

• Survey

• Statistical inference

• Census

Which sampling method allows for different homogeneous groups to be represented?

• Stratified sampling

• Simple random sampling

• Systematic sampling

• Cluster sampling

According to the Central Limit Theorem, as the sample size increases, the sampling distribution of the sample mean approaches.

• Uniform distribution.

• Skewed distribution.

• Normal distribution.

• Exponential distribution.

Which of the following conditions is generally required for the Central Limit Theorem to hold?

• The population must be normally distributed.

• The sample size must be at least 10.

• The sample size must be sufficiently large (typically n≥30).

• The standard deviation is unknown.

A researcher wants to estimate the average height of students in a large university. The population standard deviation of heights is known. According to the Central Limit Theorem, what happens to the standard deviation of the sampling distribution of the sample mean as the sample size increases?

• It increases.

• It decreases.

• It remains the same.

• It fluctuates unpredictably.

A population has a mean of 80 and a standard deviation of 12. If a sample of size 36 is taken, what is the standard deviation of the sampling distribution of the sample mean (the standard error)?

• 2

• 4

• 6

• 12