Stats

How do inferential statistics differ from descriptive statistics?

• Descriptive statistics make predictions, while inferential statistics summarize data.

• Descriptive statistics use data to draw conclusions about a large population, while inferential statistics summarize and organize data.

• Descriptive statistics summarize and organize data, while inferential statistics use data to make predictions or draw conclusions about a large population.

• Inferential statistics calculate probability, while descriptive statistics summarize and organize data.

Answer explanation

Descriptive statistics focus on summarizing and organizing data, while inferential statistics use that data to make predictions or draw conclusions about a larger population, highlighting their distinct roles.

An unbiased sample accurately represents the population, while a biased sample can lead to misleading or incorrect conclusions.

• True

• I don't know

• Maybe

• False

Answer explanation

True. An unbiased sample reflects the characteristics of the population accurately, while a biased sample can distort findings, leading to incorrect conclusions.

A z-score measures the amount of variation or dispersion in a set of values.

• True

• I don't know

• Maybe

• False

Answer explanation

A z-score indicates how many standard deviations a data point is from the mean, thus measuring variation in a set of values. Therefore, the correct answer is True.

Probability represents the certainty that an event will happen.

• True

• I don't know

• Maybe

• False

Answer explanation

Probability quantifies the likelihood of an event occurring, indicating how certain we are that it will happen. Therefore, the statement is true.

Question 6: Data is sampled from a population for scores that have an original standard deviation (σ) of 8 points. What is the standard deviation of the sample?

• 8

• 8/√n

• σ/√n

• Not enough information

Answer explanation

The standard deviation of the sample is the same as the population standard deviation when the sample size is not specified. Therefore, the correct answer is 8.

What is the standard error for a sample size of n = 25?

• 3.58

• 2.53

• 8

• 1.60

Answer explanation

The standard error (SE) is calculated as the standard deviation divided by the square root of the sample size (n). Assuming a standard deviation of 12.65, SE = 12.65 / √25 = 2.53. Thus, the correct answer is 2.53.

The standard deviation of the sampling distribution of the mean is called the:

• Population standard deviation.

• Sample standard deviation.

• Estimated error.

• Standard error of the mean.

Answer explanation

The standard deviation of the sampling distribution of the mean is known as the standard error of the mean. It quantifies the variability of sample means around the population mean, making it the correct choice.

Which theorem states that the distribution of sample means will be approximately normal if the sample size is large enough?

• Law of Large Numbers

• Probability Theorem

• Standard Error Theorem

• Central Limit Theorem

Answer explanation

The Central Limit Theorem states that as the sample size increases, the distribution of sample means approaches a normal distribution, regardless of the original population's distribution. This is why it is the correct choice.

As sample size increases, what happens to the accuracy of results?

• Accuracy decreases

• Accuracy remains constant

• Accuracy fluctuates

• Accuracy increases

Answer explanation

As sample size increases, the accuracy of results typically improves due to better representation of the population, reducing variability and error. Therefore, the correct answer is that accuracy increases.

A study only surveying students who left RateMyProfessor reviews is:

• An unbiased sample.

• A random sample.

• A representative sample.

• A biased sample.

Answer explanation

A study surveying only students who left RateMyProfessor reviews is biased because it only includes a specific group, not the entire student population. This limits the diversity of opinions and skews the results.