Lecture 13: Review One-Sample z-test and One-Sample t-test 2011, 11, 1

Statistical Test 1. How to tell if it is a one-sample z-test or one- sample t-test? 2. What are t-distributions? 3. How to conduct a one-sample t-test? 4. When to reject the null hypothesis?

One-Sample z-Test When the population mean (  ) and Std. Dev. (  ) are KNOWN, we use one-sample z-test to compare a single sample mean to the known population mean (  ). Key: Look for Population Std. Dev. (  )

One-Sample t-Test When the population Std. Dev. (  ) is UNKNOWN, we use one-sample t-test to compare a single sample mean to the known population mean (  ). We use the sample standard deviation (S) to estimate the Std. Err. Key: Look for Population Std. Dev. (  )

Population: By guessing  = 10  = ? = sample mean n = 9 Probability Mean Distribution of Sample Means:

Distribution of Sample Means: t – Distributions n > 100, Normal Distribution n = 9; df = 9 – 1 = 8 n = 70, df = 70-1 = 69

Determine 1-Tailed or 2-Tailed Test Key 1: Look at the alternative hypothesis (H 1 :  > 10) Key 2: Draw the distribution

Critical Region for One-Tailed Test p <.01 p <.05  =.05  =.01 Critical region

Determine 1-Tailed or 2-Tailed Test Key 1: Look at the alternative hypothesis (H 1 :   3) Key 2: Draw the distribution

Critical Regions for Two-Tailed Test p =.005 p =.025 p =.005  =.01  =.05

Recap today ’ s lecture 1. How to tell if it is a one-sample z-test or one-sample t-test? 2. What are t-distributions? 3. How to conduct a one-sample t-test? 4. When to reject the null hypothesis?