Statistical Tests and Hypothesis Testing

The video introduces test statistics, focusing on z-scores and t-tests, to determine if observed differences are due to random variation or actual effects. It explains how z-scores help quantify differences relative to expectations and how z-tests and t-tests are used in hypothesis testing. The video also compares critical values and p-values, emphasizing their equivalence in determining statistical significance.

What is the primary purpose of test statistics?

• To quantify how close data is to our expectations or theories

• To measure the exact value of a sample

• To calculate the median of a dataset

• To determine the mean of a population

Why is a difference of 1 second more meaningful among elite Olympic athletes compared to recreational swimmers?

• Because elite athletes have less variance in their performance times

• Because recreational swimmers are faster

• Because 1 second is a significant amount of time

• Because elite athletes swim longer distances

What does a z-score of 2 indicate in the context of IQ scores?

• The IQ score is 2 points below the mean

• The IQ score is 2 points above the mean

• The IQ score is 2 standard deviations below the mean

• The IQ score is 2 standard deviations above the mean

What is the null hypothesis in the context of the flu vaccine example?

• There is no difference in flu rates between vaccinated and unvaccinated groups

• The flu vaccine is 100% effective

• The flu vaccine causes the flu

• There is a significant difference in flu rates between vaccinated and unvaccinated groups

What is the critical value for a z-test with an alpha level of 0.05?

• 2.33 and -2.33

• 2.58 and -2.58

• 1.64 and -1.64

• 1.96 and -1.96

When should a t-test be used instead of a z-test?

• When the sample size is very large

• When the population standard deviation is unknown

• When comparing proportions

• When the sample mean is zero

What does a t-distribution have compared to a z-distribution?

• Thinner tails

• No tails

• Equal tails

• Thicker tails

What does a p-value less than 0.05 indicate?

• The test statistic is invalid

• The sample mean is zero

• The null hypothesis is true

• The sample is in the top 5% of extreme samples

What is the rhyme to remember when to reject the null hypothesis?

• Reject H-Oh if the z is too high

• Reject H-Oh if the t is too low

• Reject H-Oh if the p is too low

• Reject H-Oh if the p is too high

Why do we often use p-values instead of critical values?

• Because critical values are not reliable

• Because p-values are easier to calculate

• Because p-values are more accurate

• Because p-values are consistent across different test statistics