Introduction to Statistics in Psychology: PSY 201 - Department of ...

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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 µ = 50 with a standard deviation of σ = 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 α = 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 α = 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 µ = 70. a) If the writing scores for the population have a standard deviation of σ = 20, does the sample provide 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 a significant 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 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 µ = 50 and a standard deviation of σ = 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 α = 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 µ = 50 with a standard deviation of σ = 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 α = 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 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 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 µ = 100 and a stanard deviation of σ = 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 α = 0.01 (10) Compute the t values that form the boundaries of the critical region for a two-tailed test with α = 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 µ = 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 H 0 and conclude that the treatment has a significant effect using a two-tailed test with α = 0.05 b) If there are n = 16 individuals in the sample, are the data sufficient to reject H 0 and conclude that the treatment has a significant effect Again, assume a two-tailed test with α = 0.05. (12) Last fall, a sample of n = 36 freshmen was selected to participate in a new 4-hour training program designed to improve study skills. To evaluate the effectiveness of the new program, the sample was compared with the rest of the freshman class. All freshmen must take the same English Language Skills course, and the mean score on the final exam for the entire freshman class of µ = 75. The students in the new program had a mean score of X = 79.4 with a standard deviation of s = 18. a) On the basis of this data, can the college conclude that the students in the new program performed significantly better than the rest of the freshman class Use a one-tailed test with α = 0.05. b) On the basis of this data, can the college conclude that the students in the new program are significantly different from the rest of the freshman class Use a two-tailed test with α = 0.05. (13) The librarian at the local elementary school claims that, on average, the books in the library are more than 20 years old. To test this claim, a student takes a sample of n = 30 books and records the publication date for each. The sample produces an average age of X = 23.8 years with a variance of s 2 = 67.5. Use this sample to conduct a one-tailed test with α = 0.01 to determine whether the average age of the library books is significantly greater than 20 years.
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