PSY 201 1 Introduction to Statistics in Psychology PSY 201 Greg Francis PhD Department of Psychological Sciences Psychological Sciences Building Room 3174 765 494 6934 email gfrancis purdue edu http www1 psych purdue edu gfrancis Classes PSY201 Homework 13 Due 19 November 2009 Hand in your answers on a separate sheet of paper 1 A researcher is investigating the effectiveness of a new medication for lowering blood pressure for individuals with systolic pressure greater than 140 For this population systolic scores average average 160 with a standard deviation of 20 and the scores form a normal shaped distribution The researcher plans to select a sample of n 25 individuals and measure their systolic blood pressure after they take the medication for 60 days If the researcher uses a twotailed test with 0 05 a What is the power of the test if the medication has a 5 point effect b What is the power of the test if the medication has a 10 point effect 2 Explain how the power of a hypothesis test is influenced by each of the following Assume that all other factors are held constant a Increasing the level from 0 01 to 0 05 b Changing from a one tailed to a two tailed test 3 A researcher expects a treatment to increase scores by 5 points The regular population without treatment averages 40 with a standard deviation of 8 and the scores form a normal distribution If the researcher uses a one tailed test with 0 01 a What is the power of the test for a sample of n 16 b What is the power of the test for a sample of n 64 4 The chairman of the Federal Aviation Administration has asked a training subcommittee to investigate the current regulations for issuing licenses to sailplane pilots The null hypothesis to be tested is that the average number of hours of solo flights before awarding a license regardless of the length of the flights equals 40 that is H0 40 Assume that the standard deviation in the population is 12 5 The subcommittee is concerned with making a Type II error only if the average number of flights is more than two flights below this hypothesized value Thus the effect size ES equals 2 and the null and specific alternative hypotheses are H0 40 Ha 38 a For 0 05 and n 140 determine the power of a one tailed hypothesis test b For 0 05 and n 140 determine the power of a two tailed hypothesis test PSY 201 2 5 The president of a major educational foundation is investigating the average salary of faculty members in major state universities across the US He decides to test the null hypothesis H0 56 000 and is concerned with making a Type II error only if the average salary is less than 6000 above this hypothesized value The specific alternative hypothesis is Ha 62 000 Assume that the population standard deviation is 9 600 Determine the appropriate sample size given the following conditions and requirements a For 0 05 and 0 20 for a two tailed test b For 0 01 and 0 05 for a two tailed test c For 0 05 and 0 20 for a one tailed test 6 An industrial psychologist is studying the productivity of employees in small industries with end of the year pay incentives and those in small industries without such incentives Based on previous research the psychologist assumes the variance of productivity scores is 2 250 In a study to test whether the incentives make a difference the research will test the null hypothesis H0 1 2 0 by taking independent random samples of the same size from each population Determine the appropriate sample size given the following conditions a For 0 05 0 20 ES 12 5 for a two tailed test b For 0 01 0 05 ES 8 5 for a two tailed test c For 0 05 0 20 ES 12 5 for a one tailed test