A researcher tests five individuals who have seen paid political ads about a particular issue. These individuals take a multiple-choice test about the issue in which people in general (who know nothing about the issue) usually get 40 questions correct. The number correct for these five individuals was 48, 41, 40, 51, and 50.
Using the .05 level of significance, two-tailed, do people who see the ads do better on this test?
(a) Use the steps of hypothesis testing.
(b) Sketch the distributions involved.
(c) Explain your answer to someone who is familiar with the Z test but is unfamiliar with t tests.
A program to decrease littering was carried out in four cities in California’s Central Valley starting in August 2016. The amount of litter in the streets (average pounds of litter collected per block per day) was measured during the July before the program was started and then the next July, after the program had been in effect for a year. The results were as follows:
City July 2016 July 2017
Fresno 9 2
Merced 10 4
Bakersfield 8 9
Stockton 9 1
8.1-17 Full Alternative Text
Using the .01 level of significance, was there a significant decrease in the amount of litter?
(a) Use the five steps of hypothesis testing.
(b) Sketch the distributions involved.
(c) Explain your answer to someone who understands mean, standard deviation, and variance but knows nothing else about statistics.
Figure the estimated effect size and indicate whether it is approximately small, medium, or large, for each of the following studies:
Study Mean Change S S
(a) 20 32 32
(b) 5 10 10
(c) .1 .4 .4
(d) 100 500 500
What is the power of each of the following studies, using a t test for dependent means (based on the .05 significance level)?
Study Effect Size N Tails Tails
(a) Small 20 One One
(b) Medium 20 One One
(c) Medium 30 One One
(d) Medium 30 Two Two
(e) Large 30 Two Two
About how many participants are needed for 80% power in each of the following planned studies that will use a t test for dependent means with p<.05?
Study Predicted Effect Size Tails Tails
(a) Medium Two Two
(b) Large One One
(c) Small One One
