Exam 5: Hypothesis Tests With Means of Samples

A psychology professor of a large class became curious as to whether the students who turned in tests first scored differently from the overall mean on the test.The overall mean score on the test was 75 with a standard deviation of 10; the scores were approximately normally distributed.The mean score for the first 20 students to turn in tests was 78.Using the .05 significance level,was the average test score earned by the first 20 students to turn in their tests significantly different from the overall mean? a.Use the five steps of hypothesis testing. b.Sketch the distributions involved. c.Advanced topic: Figure the confidence limits for the 95% confidence interval. d.Explain the logic of what you did to a person who understands hypothesis testing for studies in which the sample consists of a single individual but is unfamiliar with hypothesis testing involving a sample of more than one individual.Be sure your explanation includes a discussion of the distribution of means-what it is,the logic of how it is figured-and its role in the overall hypothesis testing process.Advanced topic: Explain the logic and computation of the confidence intervals.

The variance of a distribution of means is smaller than the original population variance because

An experimental psychologist is interested in whether the color of an animal's surroundings affects learning rate. He tests 16 rats in a box with colorful wallpaper. The average rat (of this strain) can learn to run this type of maze in a box without any special coloring in an average of 25 trials, with a variance of 64, and a normal distribution. The mean number of trials to learn the maze, for the rats tested with the colorful wallpaper, is 11. -If the mean score of the sample is more extreme than the cutoff score on the comparison distribution,the psychologist will conclude that

use the following information. A population is normally distributed with μ = 50,σ = 8,and N = 10. -The mean of the distribution of means = __________.

use the following information. One hundred people are included in a study in which they are compared to a known population that has a mean of 73,a standard deviation of 20,and a rectangular distribution. -__________.

use the following information. A population is normally distributed with μ = 50,σ = 8,and N = 10. -The variance of the distribution of means = __________.

Which of the following statistics would be the most likely to appear in a research article?

A manufacturer who is considering the implementation of a one-week training program for all new employees decides to test the program with the next 100 employees hired, and then compare their productivity rate to the productivity rate of new employees based on past records—a rate that is normally distributed with a mean of 60 and a standard deviation of 8. The new program needs to produce a minimum improvement of 4 to be considered worthwhile. -What is the predicted mean of the experimental distribution?

A school psychologist interested in the effect of a program designed to reduce adjustment problems in newly transferred students knew from her years of working at the school that the average score on a scale of adjustment difficulties for transfer students was 58 with a standard deviation of 10.After starting the program,the psychologist tested 50 students and found their mean to be 52.Using the .01 level of significance,was this difference significant? a.Use the five steps of hypothesis testing. b.Sketch the distributions involved. c.Advanced topic: Figure the confidence limits for the 99% confidence interval. d.Explain the logic of what you did to a person who understands hypothesis testing for studies in which the sample consists of a single individual but is unfamiliar with hypothesis testing involving a sample of more than one individual.Be sure your explanation includes a discussion of the distribution of mean-what it is,the logic of how it is figured-and its role in the overall hypothesis testing process.Advanced topic: Explain the logic and computation of the confidence intervals.

A result that is significant at p < .10 may be referred to as __________.

The head of public safety notices that the average driving speed at a particular intersection averages 35 mph with a standard deviation of 7.5 mph.After a school speed limit sign of 20 mph is placed at the intersection,the first 40 cars travel past at an average speed of 32 mph.Using the .01 significance level,was there a significant change in driving speed? a.Use the five steps of hypothesis testing. b.Sketch the distributions involved. c.Advanced topic: Figure the confidence limits for the 99% confidence interval. d.Explain the logic of what you did to a person who understands hypothesis testing for studies in which the sample consists of a single individual but is unfamiliar with hypothesis testing involving a sample of more than one individual.Be sure your explanation includes a discussion of the distribution of means-what it is,the logic of how it is figured-and its role in the overall hypothesis testing process.Advanced topic: Explain the logic and computation of the confidence intervals.