ELEMENTARY STATISTICS, BLUMAN z Test Between Means using TI Calculator © 2019 McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom.  No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.

Objectives for this PowerPoint Conduct a z-Test about the difference between two means using the P-value method Use the TI Graphing Calculator to find the P-value

Previous PowerPoint In a previous PowerPoint we conducted a hypothesis z-Test to see if a difference existed between the mean public school teacher pay for the 2013-2014 school year for public school teachers in Mississippi and public school teachers in South Dakota. We also discussed the assumptions that must be verified for the z-Test to determine the difference between means. We will now use the P-value method to conduct the same hypothesis test. We will use the TI graphing calculator to find the P-value. In order to do so we will need to organize some of the information from the problem.

Example According to the 2016 World Almanac, the two states with the lowest average public school teacher pay for the 2013-2014 school year were Mississippi and South Dakota. Suppose random samples of 45 teachers were drawn from each state. The sample mean for Mississippi was $42,187. Suppose the population standard deviation for Mississippi is $4300. The sample mean for South Dakota was $40,023. Suppose the population standard deviation for South Dakota is $4500. At a 0.10 level of significance, is there a difference in the means of public school teacher salaries for the two states?

Data Mississippi (Group 1) South Dakota (Group 2) 𝑥 =42187 𝑥 =40023 𝜎=4300 𝜎=4500 𝑛=45

Data Needed for TI Calculator The information that we will need to input into the TI graphing calculator will be the sample means, population standard deviations, and the sample sizes for the two groups. This data is summarized on the previous slide. We will also need to specify in the TI graphing calculator that this will be a two-tailed test.

Find the P-Value (1) Press stat

Find the P-Value (2) Cursor over to TESTS This is a 2-Sample Z-test Press 3

Find the P-Value (3) Enter the data for Group 1 and Group 2. This is a two- tailed test. Make sure you highlight μ1≠μ2.

Find the P-Value (4) Cursor down to Calculate and press enter.

Find the P-Value (5) The P-value is 0.0197 Recall that the rule for using the P-value in hypothesis testing is that if the p-value is less than alpha, we should reject the null hypothesis. Since the P-value of 0.0197 is less than our significance level of 0.10. In this case we should reject the null hypothesis.

Conclusion Our conclusion is that at a 0.10 level of significance there is enough evidence to support the claim that there exists a difference in the means of public school teacher salaries for the two states.

Summary In this PowerPoint we learned how to conduct a z-Test about the difference between two means using the P- value method. We also learned how to use the TI graphing calculator to find the P-value.