An educator conducted an experiment to test whether new directed reading activities in the classroom will help elementary school pupils improve their reading ability. She arranged for a third grade class of 21 randomly selected students to follow these activities for an 8-week period. A control classroom of 23 randomly selected third graders followed the same curriculum without the activities. None of the participating students knew what class (activities or not) they belong to. At the end of the 8 weeks, all students took a Degree of Reading Power (DRP) test. Assume that the samples are independent, and the distribution of DPR Scores follows normal distribution.
Group
|
DPR Score
|
Treated
|
24
|
Treated
|
43
|
Treated
|
58
|
Treated
|
71
|
Treated
|
43
|
Treated
|
49
|
Treated
|
61
|
Treated
|
44
|
Treated
|
67
|
Treated
|
49
|
Treated
|
53
|
Treated
|
56
|
Treated
|
59
|
Treated
|
52
|
Treated
|
62
|
Treated
|
54
|
Treated
|
57
|
Treated
|
33
|
Treated
|
46
|
Treated
|
43
|
Treated
|
57
|
Control
|
42
|
Control
|
43
|
Control
|
55
|
Control
|
26
|
Control
|
62
|
Control
|
37
|
Control
|
33
|
Control
|
41
|
Control
|
19
|
Control
|
54
|
Control
|
20
|
Control
|
85
|
Control
|
46
|
Control
|
10
|
Control
|
17
|
Control
|
60
|
Control
|
53
|
Control
|
42
|
Control
|
37
|
Control
|
42
|
Control
|
55
|
Control
|
28
|
Control
|
48
|
Math 140 Project Steps:
1. Before doing any statistical analysis or looking carefully at the values in your data, ponder what the data might show and develop one interesting hypotheses that you will evaluate in your project.
For example, suppose your data gives the diameters for samples of two different kinds of trees, perhaps two species of rubber trees in a tropical rain forest. Suppose one kind grows in shadier locations and the other grows in sunnier locations. You might speculate that the species that grows in sunnier locations tends to be larger than the other species. More specifically, you could make a hypothesis that the mean diameter of all the rubber trees in the species that grows in sunny conditions is larger than the mean diameter of all the rubber trees in the species that grows in shady conditions.
It can be speculated that the average Degree of Reading Power (DRP) will be higher for students who took the new directed reading activities rather than the students who did not take the new activities.
2. As you have learned, there are several ways to display data on quantitative variables graphically. Input your data into StatCrunch. Then choose and produce at least two types of graphical displays that are appropriate for your data. Summarize the key features of each distribution, and then discuss how the two distributions compare. Discuss the extent to which this comparison supports the hypothesis you made in part 1.
Frequency of DPR Scores for Treated Students :
Frequency of DPR Scores for Control Students :
3. Please answer the indicated questions below:
1. Did your data come from an experiment or observational study?
The data collected is from an experiment. One of the groups had a treatment placed on them.
2. Identify the observational/experimental units.
The observation/experimental unit is the Degree of Reading Power (DRP) score.
3. What is your response variable?
The response variable or dependent variable is the DPR score of the students.
4. What is your explanatory variable?
The explanatory or independent variable would be the curriculum and activities.
5. Was a random assignment used?
Yes, the third graders were randomly assigned into groups.
6. Was the experiment blind? Double-blind?
The experiment is blind, the third-graders are unaware of what class (activities or not) they belong to
7. Suggest some lurking variables that could confound any cause and effect conclusions that you would ultimately like to draw from your study.
Lurking variables that may have an effect on students DPR can be studying, sleep, and if they had breakfast.
8. Describe a modification of the study design that could control for at least one of these possible lurking variables.
A modification to the study can be a quick question asking if the students had a sufficient breakfast, that way we can test if this has an effect on DPR scores.
4. Do your data come from random samples of populations? Identify the populations involved. As you have learned, the inferential methods (confidence intervals and tests) on quantitative methods that you are learning in this class depend on the assumption that your data are from a population in which the variable involved is at least approximately normally distributed. Based on the graphical displays you made in part 1, are the data approximately bell-shaped?
The data does come from random samples of populations. The data provided is approximately bell shaped.
5. In part 1 of this project you developed one hypothesis that you would evaluate in your project. In this phase you will define the populations of interest and the parameters that pertain to your analysis, and then you will estimate your parameter(s). Here is an example to show how to define your populations and parameters:
Suppose that your data gives the diameters for samples of two different species of rubber trees that grow in a tropical rain forest. One kind grows in shadier locations and the other grows in sunnier locations. Suppose that in part 1 you made the hypothesis that the species that grows in sunnier locations tends to be larger that the species that grows in shadier locations. Specifically, you may then hypothesize that the mean diameter of all the rubber trees in the species that grows in sunny conditions is larger than the mean diameter of all the rubber trees in the species that grows in shady conditions. Then your populations are:
Population1: All trees in the species that grows in sunnier conditions
Population 2: All trees in the species that grows in shadier conditions
and your parameters are:
mean diameter of all trees in the species that grows in sunnier conditions
mean diameter of all trees in the species that grows in shadier conditions
1. Define your populations of interest (Population 1 and Population2)
Population 1: All third graders selected to follow activities for an 8-week period.
Population 2: All third graders that followed the same curriculum without the activities
2. Define your population parameters (Parameter 1 and Parameter 2). Make sure to use symbols as well as words.
Parameter 1: The mean DPR score of students having extra activities (treated).
Parameter 2: The mean DPR score of students following the same curriculum without the activities (Control).
3. Give a point estimate (statistic) of each parameter.
Parameter 1: Treated Students Mean DPR score: 51
Parameter 2: Control Students Mean DPR score: 42
4. Give an interval estimate of each parameter. Show your work, and use a 95% level of confidence.
5. Give a clear and in context interpretation of what each of your confidence intervals says.
6. In this part you will use the formal methods of statistical inference to assess your hypotheses through comparisons.
1. (a) Find a confidence interval for the difference between the two parameters (means) that you analyzed individually in part 5. Use 95% level of confidence. (b) Give a clear, in-context interpretation your confidence interval.
2. (a) Use a hypothesis test to test whether the difference between your means is zero, against an alternative appropriate to the original hypothesis you made in part 1 of this project. Choose a significance level before calculating the test statistic, and be sure to report it. (b) Give a clear, in-context conclusion based on the results of (a). Do not just say "We reject the hypothesis..." or "We do not reject the hypothesis...", rather, indicate the strength of the evidence supporting your original hypothesis from part 1.
3. Are the results of #1 and #2 reasonably consistent with each other in terms of whether they support or tend to refute your original hypothesis? Discuss this briefly.