Explain at least one way that statistics can be used by an organization or a professional in a business context. Additionally, explain how statistics can be used in another context, such as in education, in the community, or in recreational activities. Your response should be 75–150 words (1–2 paragraphs).Be sure to reference at least one scholarly source to support your answer.
Part A
For each of the following scenarios, please identify the research design methodology label which might apply to the particular study. Just to remind you, these include:
Descriptive (Survey)
Descriptive (observational)
Comparative Causal
Comparative
Correlational
Quasi-Experimental
True Experimental
1. The researchers hypothesized that peer evaluation as part of the writing process would lead to improved attitude toward writing and increased fluency in a sample of ninth grade students. Seven (7) intact classrooms taught by three (3) different teachers were randomly assigned to treatment and comparison groups so that each teacher had one class in each condition. Both groups wrote a first draft of a paper. The treatment group received peer evaluation training and rewrote their papers based upon assistance from their peer evaluation group. The control group rewrote their papers receiving assistance from the teacher only when they requested help. The subjects responded to two (2) attitude instruments as pretest and posttest measures. A significant increase in positive attitudes toward writing was observed for the treatment group. Writing fluency was measured by a count of words on pre- and post-treatment drafts. There was a decrease in word count from the first to the last draft for the treatment group.
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2. This study examined factors which predict performance on the National Teacher Examinations (NTE) Core Battery. The researchers found strong relationships between a student’s undergraduate grade-point average (GPA), American College Test (ACT) subtests, and the NTE Core Battery tests.
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3. This study was intended to identify high school students’ attitudes toward school policies and practices. Subjects were given a rating scale instrument listing specific school policies and asked to rate each one on a 5-point scale ranging from “strongly disagree” to “strongly agree.” A typical sample item being rated is as follows: “Students in my school are given enough responsibility in establishing rules of conduct.”
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4. This study was intended to identify the types and effectiveness of various forms of positive teacher reinforcement. Teams of researchers developed checklists of such positive behaviors and recorded types and frequency of occurrence in a sample of classroom sessions they attended.
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5. The purpose of the study was to determine if Method A of teaching reading would produce superior results in terms of reading comprehension than Method B. One thousand (1,000) second graders were randomly chosen to participate in the study. These second graders were then randomly assigned to either Method A or Method B. Both groups were given a baseline pretest of reading comprehension, as well as the same posttest.
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6. A researcher is interested in finding out if children who have attended nursery school perform better in reading in the first grade than those who have not attended nursery school. He/she compares the mean reading scores of both groups.
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7. The purpose of this study was to determine if selected students whose homes were called, using a computer-assisted telecommunications device, on days when they were not in school would show an expected difference in school attendance, as compared with selected students whose homes were not called. One hundred and fifty (150) students were chosen at random at the beginning of the school year to serve as the baseline group. No calls were made to the students to were absent in this baseline group. The same random selection procedure was followed for selecting the one hundred and fifty (150) students in the “treatment” group. For this group, each of the students was called at the end of the day(s) for which he/she was absent from school, using the automatic dialing device.
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(HINT: Think about ‘researcher’s power to ‘form’ groups here! This one is a bit ‘subtle’ in that regard!)
8. This study was intended to determine how much knowledge of world geography children have in the third grade. To address this problems statement, students in the sample were administered a paper-and-pencil questionnaire containing basic geography concepts.
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9. A teachers’ union wishes to determine whether there is a difference between elementary and secondary teachers in their propensity to run for and assume office. This information (numbers of elementary and secondary teachers who have run for, and/or assumed, office) is obtained from the school district office records, and appropriate statistical tests of between-group difference are run on these data.
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10 The same teachers’ union also wishes to determine if there is a relationship between the number of union meetings that teachers attend, and the length (in years) that they have been members of the union.
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Part B
2. In each of the following, indicate whether the result or relationship is likely to be practically significant and then explain your reasoning:
(a) A researcher finds that a particular relationship can occur by chance about 20 times in 100
(b) A researcher finds that students who use a new biology textbook recently purchased by the school district scored an average of 20 percent higher on an end-of-the course examination
(c) A researcher finds that use of a certain drug decreases the incidence of a life-threatening illness among a group of senior citizens by 3 percent
(d) A small appliance store owner finds that advertising in the local neighborhood newspaper increases her sales each week by 1 percent
(e) A new method of teaching five-year olds how to tie their shoes results in their being able to do so three weeks earlier than similar five-year olds not taught by this method
(f) A researcher finds that a correlation of .18 has only a 1 in 1,000 likelihood of occurring by chance
A wholesale distributor operating in different regions of Portugal has information on annual spending of several items in their stores across different regions and channels. The data (Wholesale Customer.csv) consists of 440 large retailers’ annual spending on 6 different varieties of products in 3 different regions (Lisbon, Oporto, Other) and across different sales channel (Hotel, Retail).
1.1. Use methods of descriptive statistics to summarize data.
Which Region and which Channel seems to spend more?
Which Region and which Channel seems to spend less?
1.2. There are 6 different varieties of items are considered.
Do all varieties show similar behaviour across Region and Channel?
1.3. On the basis of the descriptive measure of variability, which item shows the most inconsistent behaviour?
Which items shows the least inconsistent behaviour?
1.4. Are there any outliers in the data?
1.5. On the basis of this report, what are the recommendations?
Problem 2
The Student News Service at Clear Mountain State University (CMSU) has decided to gather data about the undergraduate students that attend CMSU. CMSU creates and distributes a survey of 14 questions and receives responses from 62 undergraduates (stored in the Survey.csv file).
Part I
- 2.1. For this data, construct the following contingency tables (Keep Gender as row variable)
2.1.1. Gender and Major
2.1.2. Gender and Grad Intention
2.1.3. Gender and Employment
2.1.4. Gender and Computer - 2.2. Assume that the sample is a representative of the population of CMSU. Based on the data, answer the following questions:
2.2.1. What is the probability that a randomly selected CMSU student will be male?
What is the probability that a randomly selected CMSU student will be female?
2.2.2. Find the conditional probability of different majors among the male students in CMSU.
Find the conditional probability of different majors among the female students of CMSU.
2.2.3. Find the conditional probability of intent to graduate, given that the student is a male.
Find the conditional probability of intent to graduate, given that the student is a female.
2.2.4. Find the conditional probability of employment status for the male students as well as for the female students.
2.2.5. Find the conditional probability of laptop preference among the male students as well as among the female students. - 2.3. Based on the above probabilities, do you think that the column variable in each case is independent of Gender?
Justify your comment in each case.
Part II
- 2.4. Note that there are three numerical (continuous) variables in the data set, Salary, Spending and Text Messages. For each of them comment whether they follow a normal distribution.
Write a note summarizing your conclusions.
[Recall that symmetric histogram does not necessarily mean that the underlying distribution is symmetric]
Problem 3
An important quality characteristic used by the manufacturers of ABC asphalt shingles is the amount of moisture the shingles contain when they are packaged. Customers may feel that they have purchased a product lacking in quality if they find moisture and wet shingles inside the packaging. In some cases, excessive moisture can cause the granules attached to the shingles for texture and colouring purposes to fall off the shingles resulting in appearance problems. To monitor the amount of moisture present, the company conducts moisture tests. A shingle is weighed and then dried. The shingle is then reweighed, and based on the amount of moisture taken out of the product, the pounds of moisture per 100 square feet is calculated. The companyclaimsthat the mean moisture contentcannot be greaterthan 0.35 pound per 100 square feet.
The file (A & B shingles.csv) includes 36 measurements (in pounds per 100 square feet) for A shingles and 31 for B shingles.
For the A shingles, the null and alternative hypothesis to test whether the population mean moisture content is less than 0.35 pound per 100 square feet is given:
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HA” style=”box-sizing: inherit; max-width: 100%; height: auto;”>>0.35
For the B shingles, the null and alternative hypothesis to test whether the population mean moisture content is less than 0.35 pound per 100 square feet is given:
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HA” style=”box-sizing: inherit; max-width: 100%; height: auto;”>>0.35
3.1 Do you think that the population means for shingles A and B are equal? Form the hypothesis and conduct the test of the hypothesis. What assumption do you need to check before the test for equality of means is performed?
3.2 What assumption about the population distribution is needed in order to conduct the hypothesis tests above?