Introduction to t Statistics

These flashcards cover key concepts and definitions from the lecture on t statistics, including the differences between t and z tests, the role of degrees of freedom, Cohen's d, and the steps involved in hypothesis testing.

What is the primary difference between the t and z statistics?

The t statistic is used when the population standard deviation is unknown and is computed using the sample standard deviation.

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

A t-test should be used when the population standard deviation is unknown and when comparing sample means.

What does estimated standard error (sM) replace in the t-test?

Estimated standard error (sM) replaces the real standard error (σM) when the population standard deviation is unknown.

Who invented the t statistic and why?

William Sealy Gosset invented the t statistic to help Guinness test the quality of their beer.

What does the critical score indicate in hypothesis testing?

The critical score defines the threshold beyond which the sample mean is significantly different from the population mean.

What are degrees of freedom (df) in the context of t-tests?

Degrees of freedom (df) typically refer to the sample size minus a certain number, such as N-1 for a one-sample t-test.

What is Cohen’s d and what does it measure?

Cohen's d is a measure of effect size that indicates the standardized difference between two means.

How does the distribution of sample means for the t-test compare to that for the z-test?

The distribution of sample means for the t-test has more variability than the z-test.

What are the five steps in hypothesis testing?

1. State the null and alternative hypotheses and select an alpha level. 2. Locate the critical region using the t distribution table. 3. Calculate the t test statistic. 4. Make a decision regarding the null hypothesis. 5. Interpret the results.

How is confidence interval related to hypothesis testing?

If a t-test is significant, the confidence interval will provide a range where the true population mean is likely to fall.