PSY 201 1Introduction to Statistics in Psychology: PSY 201Greg Francis, PhDDepartment of Psychological SciencesPsychological Sciences Building, Room 3174(765) 494-6934email: [email protected]://www1.psych.purdue.edu/∼gfrancis/Classes/PSY201/Homework 13Due: 19 November 2009Hand in your answers on a separate sheet of paper.(1) A researcher is investigating the effectiveness of a new medication for lowering blood pressurefor individuals with systolic pressure greater than 140. For this population, systolic scores averageaverage µ = 160 with a standard deviation of σ = 20, and the scores form a normal shapeddistribution. The researcher plans to select a sample of n = 25 individuals, and measure theirsystolic blood pressure after they take the medication for 60 days. If the researcher uses a two-tailed test with α = 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 thatall other factors are held constant.a) Increasing the α 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 µ = 40 with a standard deviation of σ = 8, and the scores form anormal distribution. If the researcher uses a one-tailed test with α = 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 toinvestigate the current regulations for issuing licenses to sailplane pilots. The null hypothesis to betested is that the average number of hours of solo flights before awarding a license (regardless ofthe length of the flights) equals 40; that is H0: µ = 40. Assume that the standard deviation in thepopulation is σ = 12.5. The subcommittee is concerned with making a Type II error only if theaverage number of flights is more than two flights below this hypothesized value. Thus, the effectsize (ES) equals -2, and the null and specific alternative hypotheses are : H0: µ = 40, Ha: µ = 38.a) For α = 0.05 and n = 140 determine the power of a one-tailed hypothesis test.b) For α = 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 facultymembers in major state universities across the US. He decides to test the null hypothesis H0: µ =56, 000 and is concerned with making a Type II error only if the average salary is less than $6000above this hypothesized value. The specific alternative hypothesis is Ha: µ = 62, 000. Assumethat the population standard deviation is σ = 9, 600. Determine the appropriate sample size giventhe following conditions and requirements:a) For α = 0.05 and β = 0.20, for a two-tailed test.b) For α = 0.01 and β = 0.05, for a two-tailed test.c) For α = 0.05 and β = 0.20, for a one-tailed test.(6) An industrial psychologist is studying the productivity of employees in small industries withend-of-the-year pay incentives and those in small industries without such incentives. Based onprevious research, the psychologist assumes the variance of productivity scores is σ2= 250. In astudy to test whether the incentives make a difference, the research will test the null hypothesisH0: µ1− µ2= 0 by taking independent random samples of the same size from each population.Determine the appropriate sample size given the following conditions.a) For α = 0.05, β = 0.20, ES = 12.5, for a two-tailed test.b) For α = 0.01, β = 0.05, ES = 8.5 for a two-tailed test.c) For α = 0.05, β = 0.20, ES = 12.5, for a one-tailed