MATH 2050 Project Guidelines
Your grade will be determined by the paper you hand in and the presentation you give.

Your population of interest will be all MTSU students.
For the simplicity’s sake, we will use our class as our “random” sample.

Your tasks:

Data Collection:
•Determine 4 to 6 variables (at least 2 quantitative and 2 qualitative) you would like to collect information on from the sample. •Write a survey that asks clear questions that will allow you to collect your data. Type this survey up in (with your name somewhere at the top) and print 45 copies.

Research Questions:
•Write at least 3 research questions about the population that can be answered from your data. Two or more of these questions should be able to be answered by a hypothesis test (these questions will investigate relationships between variables) and one or more could be answered from a confidence interval (this question will investigate the true value of an unknown parameter).

Data Analysis:
Conduct appropriate data analysis techniques to answer your research questions. This analysis should include two or more hypothesis tests, can include one confidence interval, and should include at least one graph. (If you don’t do a confidence interval, you should do at least 3 hypothesis tests.)

Paper:
Write a paper that includes the following:
•An introduction that gives an overview of the big idea of your project and the research questions you sought to answer •A methods section that clearly states your methodology (what data did you collect, how did you collect it, and how do you plan to analyze it?) •A results section that clearly states how you analyzed the data (clearly report the results of your data analysis… include graphs and tables where necessary… give the specifics of the results of your data analysis here (p-values, etc.)) •A conclusion section that discusses how your data analysis informed your research questions. Include limitations of your...

...Hypothesistesting
Use of hypothesistesting can be very useful during decision-making connected with statistical data. A hypothesis is a statement made about a population parameter e.g. a mean and variance of a population. Hypothesistesting is a statistical process, which gives ideas or theories and then determine whether these ideas are true or false. The conclusions inhypothesistesting never 100%, therefore all tested ideas can be only probably true or probably false.
One of the most important concepts in hypothesistesting is sampling distribution.
Sampling distribution is a probability distribution of sample statistics based on all possible random samples. We have to choose randomly some amount of samples to conduct testing. The more samples size we take the better our sample curve looks normally distributed. Difference between the sample mean and population mean is a sampling error. The less this error the better result of testing. Usually we take 30 samples, which are enough to draw normally distributed curve.
Typical use scenario below will make clear the real life situation when we may use Hypothesistesting:
A bottled water manufacturer states on the product label that each of bottle contains 500 ml of water. We work for the government agency...

...all, the video did a fair job buttressing my understanding of hypothesistesting. The textbook explained the aspects and steps of hypothesistesting in a legible fashion, while the video helped demonstrate a real-life application.
I learned from the text that hypothesistesting is a “Procedure for deciding whether the outcome of a study (results from a sample) supports a particular theory or practical innovation (which is thought to apply to a population)” (Aron A., Aron, E., and Coups, 2011, p. 145). I also learned that hypothesistesting follows a set procedure that appears as follows:
Step 1) Restate the question as a research hypothesis and a null hypothesis about the populations
- Basically, a researcher constructs a hypothesis. Then he/she forms a null hypothesis that opposes the research hypothesis in
polar fashion. To help support one’s research hypothesis, one has to disprove the null hypothesis.
Step 2) Determine the characteristics of the comparison distribution
- When using two or more samples, one must gather information about the distribution of means.
Step 3) Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected
- Most researchers...

...Elements of a Test of Hypothesis 1. Null Hypothesis (H0 ) - A statement about the values of population parameters which we accept until proven false. 2. Alternative or Research Hypothesis (Ha )- A statement that contradicts the null hypothesis. It represents researcher’s claim about the population parameters. This will be accepted only when data provides suﬃcient evidence to establish its truth. 3. Test Statistic - A sample statistic (often a formula) that is used to decide whether to reject H0 . 4. Rejection Region- It consists of all values of the test statistic for which H0 is rejected. This rejection region is selected in such a way that the probability of rejecting true H0 is equal to α (a small number usually 0.05). The value of α is referred to as the level of signiﬁcance of the test. 5. Assumptions - Statements about the population(s) being sampled. 6. Calculation of the test statistic and conclusion- Reject H0 if the calculated value of the test statistic falls in the rejection region. Otherwise, do not reject H0 . 7. P-value or signiﬁcance probability is deﬁned as proportion of samples that would be unfavourable to H0 (assuming H0 is true) if the observed sample is considered unfavourable to H0 . If the p-value is smaller than α, then reject H0 . Remark: 1. If you ﬁx α = 0.05 for your test, then you are allowed to reject true null hypothesis 5% of the time in repeated application of your test...

...of ANOVA are identical to the t-test and the calculated statistic is called an F-value which has a probability value associated with it. As with the t-test, if our probability value is less than 0.05 we reject our null hypothesis (in this case that there is no difference among the treatment groups). This p-value only tells if there are significant differences among our groups. It does not tell us where these differences are. In other words, in an experiment with three treatment groups and a significant p value, we know that there are some differences among these groups but we do not know specifically which groups are different. As a result, ANOVA is usually performed in conjunction with a post hoc multiple comparisons test (e.g. Bonferoni’s test or Tukey’s test) that will tell you precisely where the differences lie.
A set of data can only “reject” a null hypothesis or “fail to reject it”. In our case, if comparison of three groups (10-mg treatment, 20-mg treatment, and no treatment) reveals no statistically significant difference between the three, it does not mean that there is no difference in reality. It only means that there is not enough evidence to reject the null hypothesis (in other words, the experiment fails to reject the null hypothesis).
Analysis of variance:
Analysis of variance is used to determine if differences exist between the three treatment groups. The computation of ANOVA is...

...HYPOTHESISTESTING
WHAT IS THIS HYPOTHESIS????
• In simple words it means a mere assumption or supposition to be proved of disproved.
• But, for a researcher it is a formal question that he intends to resolve.
• Example: I assume that 1) under stress and anxiety a person goes into depression.
2) It leads to aggressive behaviour.
Eg. : Students who get better counselling in a university will show a greater increase in creativity than students who were not counselled.
• So, the hypothesis should be capable of being verified and tested.
CHARACTERISTICS
• Should be clear and precise – inferences not reliable
• Capable of being tested
“ A hypothesis is testable if other deductions can be made from it which, in turn can be confirmed or disproved by observation.”
• Should be limited in scope and must be specific
• Should be stated in simple terms -understandable by all concerned.
• Must explain the facts that gave rise to the need for explanation.
BASIC CONCEPTS: NULL & ALTERNATIVE HYPOTHESIS
• If we are to compare two methods A & B and both are equally good, then this assumption is termed as null hypothesis(H0)
• If it is stated that method A is better than method B-alternative hypothesis(Ha)
LEVEL OF SIGNIFICANCE
• A very important concept in the context of hypothesis...

...HypothesisTesting For a Population Mean
The Idea of HypothesisTesting
Suppose we want to show that only children have an average higher cholesterol level than the national average. It is known that the mean cholesterol level for all Americans is 190. Construct the relevant hypothesis test:
H0: = 190
H1: > 190
We test 100 only children and find that
x = 198
and suppose we know the population standard deviation
= 15.
Do we have evidence to suggest that only children have an average higher cholesterol level than the national average? We have
z is called the test statistic.
Since z is so high, the probability that Ho is true is so small that we decide to reject H0 and accept H1. Therefore, we can conclude that only children have a higher average cholesterol level than the national average.
Rejection Regions
Suppose that = .05. We can draw the appropriate picture and find the z score for -.025 and .025. We call the outside regions the rejection regions.
We call the blue areas the rejection region since if the value of z falls in these regions, we can say that the null hypothesis is very unlikely so we can reject the null hypothesis
Example
50 smokers were questioned about the number of hours they sleep each day. We want to test the hypothesis that the smokers need less...

...Nonparametric HypothesisTesting Paper
ABC’s real estate agency has recently expanded its business and is in the process of conducting research on housing prices within 10 miles of its new office. Team B has been given the task by ABC real estate to conduct the needed research. The team will be able to answer at the end of the research if the prices in Santa Cruz, California, are less than the prices of house in Scott’s Valley, California. Throughout this research process the team will formulate the hypothesis statement, perform a five-step hypothesis test, discuss which nonparametric test was needed, and discuss the results from this data research compare to past research completed.
Five-Step Hypothesis Test
The five-step hypothesis test will determine if consumers have a greater satisfaction when the consumer(s) pay more for the home.
Step one is to state the null hypothesis and alternative hypothesis:
Ho: µ1 = µ2 No difference in satisfaction
Ho: µ1≠ µ2 Satisfaction differs for the two groups
Step two evaluates if the assumptions have been met through the Mann-Whitney test selection that will compare the two populations and will assume equal variances with a 95% confidence level, the significance level is .05. The decision rule is to reject Ho if z>1.645.
Step three the ranks are summed and calculated using the Wilcoxon – Mann-Whitney test....

...CHAPTER 4 – THE BASIS OF STATISTICAL TESTING
* samples and populations
* population – everyone in a specified target group rather than a specific region
* sample – a selection of individuals from the population
* sampling
* simple random sampling – identify all the people in the target population and then randomly select the number that you need for your research
* extremely difficult, time-consuming, expensive
* cluster sampling – identify clustering units in the population
* opportunity sampling – selecting participants who just happen to be available at the time and the place that you are conducting your research
* snowball sampling – referrals from participants
* volunteer sampling – where you might advertise your study and wait for people who have read your ad to come forward to take part
* how generalizable are data?
* Q: are the means for our sample approximately equal to the mean from the population?
* randomly selected sample because of this random factor, sample may not be exactly representative
* sampling error
* the difference between the sample mean and the population mean
* ensure that you have enough participants so that you get an accurate reflection of the population that you are interested in
* population mean (parameter), sample mean (statistic)
* the larger the samples, the...