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 8 Due 18 October 2009 Hand 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 particular vitamin in their blood than non vegetarians An experiment is conducted and vegetarians do have more of the vitamin but the difference is not significant The probability value is 0 13 Should the experimenter 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 the probability 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 is true b What is the probability that you will make a Type I error given that the null hypothesis is false 4 Although there is a popular belief that herbal remedies such as Ginkgo biloba and Ginseng may improve learning and memory in healthy adults these effects are usually not supported by well controlled research Peresson et al 2004 In a typical study a researcher obtains a sample of n 36 participants and has each person take the herbal supplements every day for 90 days At the 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 80 and a standard deviation of 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 0 05 PSY 201 2 5 A researcher is testing the effectiveness of a new drug that is intended to improve learning and memory performance A sample of n 16 rats is obtained and the rats are administered the drug and then tested on a standardized learning task For the general population of rats with no drugs the average score on the standardized task is 50 with a standard deviation of 10 The distribution 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 this sufficient to conclude that there is a significant effect using a two tailed test with 0 05 b If there is a 6 point effect with a mean score of X 56 is this sufficient to conclude that there is a significant effect using a two tailed test with 0 05 6 State College is evaluating a new English composition course for freshmen A random sample of 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 graded using a standardized evaluation technique The average score for the sample if X 76 For the general population of college students writing score form a normal distribution with a mean of 70 a If the writing scores for the population have a standard deviation of 20 does the sample provide enough evidence to conclude that the new composition course has a significant effect Assume a two tailed test with 0 05 b If the population standard deviation is 10 is the sample sufficient to demonstrate a significant effect Again assume a two tailed test with 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 the household develop different personality characteristics than those who grow up in larger families A sample 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 50 and a standard deviation of 15 If the mean for the mean for the sample is X 58 can the researcher conclude that there is a significant difference in personality between only children and the rest of the population Use a two tailed test with 0 05 8 A researcher is testing the hypothesis that consuming a sports drink during exercise will improve endurance A sample of n 50 male college students is obtained and each student is given a series of three endurance tasks and asked to consume 4 ounces of the drink during each break between tasks The overall endurance score for this sample is X 53 For the general population without any sports drink the scores for this task average 50 with a standard deviation of 12 a Can the researcher conclude that endurance scores with the sports drink are significantly higher than scores without the drink Use a one tailed test with 0 05 b Can the researcher conclude that endurance scores with the sports drink are significantly higher than scores without the drink Use a two tailed test with 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 mathematics problems correctly when simple problems were mixed in with their regular math assignments To further explore this phenomenon suppose that a researcher selects a standardized mathematics achievement test that produces a normal distribution of scores with a mean of 100 and a stanard deviation of 18 The researcher modifies the test by inserting a set of very easy problems among the standardized questions and gives the modified test to a sample of n 36 students If the average test score for the sample is X 104 is this result sufficient to conclude that inserting the easy questions improves performance Use a one tailed test with 0 01 10 Compute the t values that form the boundaries of the critical region for a two tailed test with 0 05 for each of the following df values a df 8 b df 15 c df 24 11 A sample is randomly selected from a population with a mean of 50 and a treatment is administered to the individuals in the sample After treatment the sample is found to have a mean of X 56 with a standard deviation of s 8 a If there are n 4 individuals in the sample are the data sufficient to reject H0 and conclude that the treatment has a significant effect using a two tailed test with 0 05 b If there are n 16 individuals in the sample are the data sufficient to reject H0 and conclude