Foundations of Statistics - Tutorial Week 6 Hypothesis Testing - One-sample t-test and Binomial Test Learning Objectives V Know how to produce a One-Sample t-test in SPSS and be able to interpret the results V Know how to produce a Binomial Test in SPSS and be able to interpret the results V Understand the link between Sampling Distribution critical values and Hypothesis tests p-values Exercise 1: John is a worker within the automotive industry who has many friends in the construction industry. These friends continually bemoan that they work, on average, 40 hours a week. John believes that in the automotive industry, workers work more than 40 hours per week and wants to test this claim. He takes a random sample of workers in the automotive industry and records how many hours per week [based on the last week] they worked. In order to test the claim that automotive workers work for more than 40 hours per week, you are required to work through the process for constructing the hypothesis test, including conducting a One-Sample t-test using the Hours_Worked_Auto_Industry.sav. The questions shown below may assist you with this process. Hypothesis Test process: Step 1: identify the Null [H0] and Alternative Hypotheses [H1] Ho: Il(automotive industry hours of work) <= 40 hours H1: Il(automotive industry hours of work) > 40 hours Step 2: identify the Alpha test level [significance test level]: a = 0.050 Step 3: identify the sample statistics [t-value, df, p-value] Adjust the test value to 40. Analyze -> Compare Means and Proportions -> One-sample T-test Step 4: decide if to reject / do not reject the Null Hypothesis based on the information from Step 3 Hours_Worke d One-Sample Statistics N 80 Mean 39.3639 Std. Deviation 6.01781 Std. Error Mean .67281 One-Sample Test 1
Hours_Worked t -. 945 df Test Value = 40 Significance One- Two- Sided p Sided p Mean Difference 95% Confidence Interval of the Difference Lower Upper 79 .174 .347 -. 63613 -1.9753 .7031 t(79) = . 95, p =. 347 The t-test result is not significant because the p-value > .05 so there is no significant difference in hours worked between the sample and 40 hours. Mean difference - in the sample on average the number of hours worked by auto industry workers was . 64 less than 40 hours 95% confidence interval indicates that the average number of hours worked by auto industry workers is between 1.98 hours less and .70 hours more than the 40 hours for construction industry workers. A. What are the two populations relevant to this question? All employees of the automotive industry and all employees of the construction industry B. How many people comprise the sample? 80 C. Which population is the sample selected from? Employees in the automotive industry D. What is the mean [average] number of hours worked in the sample? M = 39.36, s = 6.02 E. Is John's hypothesis directional or non-directional? Directional F. What do the results of the one-sample t-test tell us? That