Statistics for Data Science and Business Analysis - Calculating Confidence Intervals Within a Population with an Unknown

The video tutorial explains the use of the T statistic for calculating confidence intervals when the population variance is unknown. It provides a step-by-step guide on how to find the T statistic using a T table, emphasizing the differences between using T and Z statistics. The tutorial compares confidence intervals with known and unknown variances, highlighting the increased uncertainty with unknown variance. Key learnings include the application of the T statistic and the impact of variance knowledge on confidence interval accuracy.

Why is the T statistic used instead of the Z statistic for small samples?

• Because the sample size is large

• Because the population variance is unknown

• Because the data is not normally distributed

• Because the sample mean is zero

What is a key difference between the T statistic and the Z statistic?

• T statistic uses population standard deviation

• Z statistic is used for unknown population variance

• T statistic uses sample standard deviation

• Z statistic is used for small samples

How do you determine the degrees of freedom for a T distribution?

• By using the sample mean

• By subtracting 1 from the sample size

• By subtracting 2 from the sample size

• By adding 1 to the sample size

What happens to the confidence interval when the population variance is unknown?

• It cannot be calculated

• It becomes wider

• It remains the same

• It becomes narrower

What is the confidence level used in the example for calculating the T statistic?

• 90%

• 85%

• 95%

• 99%