Understanding Z-statistics and T-statistics

This video tutorial explains the differences between Z-statistics and T-statistics, focusing on their application in inferential statistics. It covers the calculation of Z-scores using sample data, the role of the central limit theorem, and how to approximate population standard deviation with sample data. The tutorial also discusses when to use T-distribution for small sample sizes and how to interpret results using Z-tables and T-tables.

What is the main focus of inferential statistics as discussed in the video?

• Assessing the mode of a sample

• Finding the median of a dataset

• Determining the probability of a sample mean

• Calculating the mean of a population

What does the central limit theorem help us understand in the context of sampling distributions?

• The mode of the sample

• The standard deviation of the sampling distribution

• The shape of the distribution

• The mean of the population

When the population standard deviation is unknown, what can be used to approximate the Z-score?

• Population mean

• Sample mean

• Population variance

• Sample standard deviation

Under what condition is the approximation of the Z-score using the sample standard deviation considered valid?

• Sample size is equal to 15

• Sample size is greater than 30

• Sample size is exactly 20

• Sample size is less than 10

What distribution is used when the sample size is small and the data is not normally distributed?

• T-distribution

• Normal distribution

• Binomial distribution

• Poisson distribution

What is a key characteristic of a normalized T-distribution?

• Mean of 1

• Mean of 0

• Mean of -1

• Mean of 2

What is the rule of thumb for using a Z-statistic?

• Use when sample size is exactly 15

• Use when sample size is greater than 30

• Use when sample size is less than 5

• Use when sample size is less than 10

When should a T-table be used instead of a Z-table?

• When the sample size is unknown

• When the sample size is small

• When the sample size is large

• When the sample size is exactly 30

What is the main difference between a Z-statistic and a T-statistic?

• Z-statistic is always more accurate than T-statistic

• Z-statistic is used for small samples, T-statistic for large samples

• Z-statistic assumes normal distribution, T-statistic does not

• Z-statistic uses population standard deviation, T-statistic uses sample standard deviation

What is the probability of getting a Z-value or T-value at least as extreme as the observed value?

• The median of the population

• The standard deviation of the sample

• The area under the curve

• The mean of the distribution