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 8Due: 18 October 2009Hand in your answers on a separate sheet of paper.(1) A researcher develops a new theory that predicts that vegetarians will have more of a particularvitamin in their blood than non-vegetarians. An experiment is conducted and vegetarians do havemore of the vitamin, but the difference is not significant. The probability value is 0.13. Should theexperimenter’s confidence in the theory increase, decrease, or stay the same? Explain your choice.(2) A significance test is performed and p = .20. Why can’t the experimenter claim that theprobability that the null hypothesis is true is .20?(3) You choose an alpha level of .01 and then analyze your data.a) What is the probability that you will make a Type I error given that the null hypothesis istrue?b) What is the probability that you will make a Type I error given that the null hypothesis isfalse?(4) Although there is a popular belief that herbal remedies such as Ginkgo biloba and Ginsengmay improve learning and memory in healthy adults, these effects are usually not supported bywell-controlled research (Peresson et al., 2004). In a typical study, a researcher obtains a sampleof n = 36 participants and has each person take the herbal supplements every day for 90 days. Atthe end of the 90 days, each person takes a standardized memory test. For the general population,scores from the test are normally distributed with a mean of µ = 80 and a standard deviation ofσ = 18. The sample of research participants had an average of X = 84.a) In a sentence, state the null hypothesis being tested.b) Using symbols, state the null hypothesis and the alternative hypothesis.c) Conduct the hypothesis using a two-tailed test with α = 0.05.PSY 201 2(5) A researcher is testing the effectiveness of a new drug that is intended to improve learning andmemory performance. A sample of n = 16 rats is obtained, and the rats are administered the drugand then tested on a standardized learning task. For the general population of rats (with no drugs)the average score on the standardized task is µ = 50 with a standard deviation of σ = 10. Thedistribution of test scores is normal.a) If the drug has a 4-point effect and produces a mean score of X = 54 for the sample, is thissufficient to conclude that there is a significant effect using a two-tailed test with α = 0.05?b) If there is a 6-point effect with a mean score of X = 56, is this sufficient to conclude thatthere is a significant effect using a two-tailed test with α = 0.05?(6) State College is evaluating a new English composition course for freshmen. A random sampleof n = 25 freshmen is obtained and the students are placed in the course during their first semester.One year later, a writing sample is obtained for each student and the writing samples are gradedusing a standardized evaluation technique. The average score for the sample if X = 76. For thegeneral population of college students, writing score form a normal distribution with a mean ofµ = 70.a) If the writing scores for the population have a standard deviation of σ = 20, does the sampleprovide enough evidence to conclude that the new composition course has a significant effect?Assume a two-tailed test with α = 0.05.b) If the population standard deviation is σ = 10, is the sample sufficient to demonstrate asignificant effect? Again, assume a two-tailed test with α = 0.05.c) Briefly explain why you reached different conclusions for part (a) and part (b).(7) A psychologist is investigating the hypothesis that children who grow up as the only child in thehousehold develop different personality characteristics than those who grow up in larger families. Asample of n = 30 only children is obtained and each child is given a standardized personality test.For the general population, scores on the test from a normal distribution with a mean of µ = 50and a standard deviation of σ = 15. If the mean for the mean for the sample is X = 58, can theresearcher conclude that there is a significant difference in personality between only children andthe rest of the population? Use a two-tailed test with α = 0.05.(8) A researcher is testing the hypothesis that consuming a sports drink during exercise will improveendurance. A sample of n = 50 male college students is obtained and each student is given a seriesof three endurance tasks and asked to consume 4 ounces of the drink during each break betweentasks. The overall endurance score for this sample is X = 53. For the general population, withoutany sports drink, the scores for this task average µ = 50 with a standard deviation of σ = 12.a) Can the researcher conclude that endurance scores with the sports drink are significantlyhigher than scores without the drink? Use a one-tailed test with α = 0.05.b) Can the researcher conclude that endurance scores with the sports drink are significantlyhigher than scores without the drink? Use a two-tailed test with α = 0.05.c) You should find that the two tests lead to different conclusions. Explain why.PSY 201 3(9) Montarello and Martins (2005) found that fifth-grade students completed more mathematicsproblems correctly when simple problems were mixed in with their regular math assignments. Tofurther explore this phenomenon, suppose that a researcher selects a standardized mathematicsachievement test that produces a normal distribution of scores with a mean of µ = 100 and astanard deviation of σ = 18. The researcher modifies the test by inserting a set of very easyproblems among the standardized questions, and gives the modified test to a sample of n = 36students. If the average test score for the sample is X = 104, is this result sufficient to concludethat inserting the easy questions improves performance? Use a one-tailed test with α = 0.01(10) Compute the t values that form the boundaries of the critical region for a two-tailed test withα = 0.05 for each of the following df values.a) df = 8b) df = 15c) df = 24(11) A sample is randomly selected from a population with a mean of µ = 50, and a treatmentis administered to the individuals in the sample. After treatment, the sample is found to have amean of X = 56 with a standard deviation of s = 8.a) If there are n = 4 individuals in the